Catalan's Conjecture - Numberphile

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With Dr Holly Krieger from Murray Edwards College, University of Cambridge.
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Опубликовано:

29 сен 2024

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Комментарии : 1,5 тыс.

@johnayres2303 6 лет назад

I have purchased lots of brown paper and magic markers but I am still useless at Maths.

@johnayres2303 6 лет назад

Marcus Campbell Yes I know it is corny

@dangernoodle8376 6 лет назад

You need sharpies

@briandeschene8424 5 лет назад

John Ayres ...but you’re very fashionable while being useless. A Kardashian of maths.

@niemandniemand2178 5 лет назад

dumbass

@Q_QQ_Q 5 лет назад

*Dr Holly Krieger is so white and redhead that i need my dark glasses to even see* . 😂😂😂😂😂😂😂😂😂😂😂😂

@richtalk34 2 года назад

I've read that 26 is the only integer that falls directly between a square (25) and a cube (27), and that Fermat proved it? Is this right and is the proof similar to this?

@jayyyzeee6409 6 лет назад

Nicely done! Making math entertaining as always!

@arturslunga3415 3 года назад

Why is the fourth cube afraid of 1? Because 1, 8, 27.

@funkygecko 6 лет назад

Guys anyone got any quick proof on this? My professor said he would pass anyone who proved it with the highest possible mark. I failed when I tried, obviously. ps: I think he was personal friends with Mihailescu, the one who proved it.

@r_se 6 лет назад

search "an elementary proof of Catalan-Mihailescu Theorem" on google

@techwithwhiteboard3483 5 лет назад

i have a simple proof for x2 - y3 = 1 but not for y3-x2=1 🙂and its mathematical with symbols and concrete logic unlike here which says 2 cubes cant be close ofcourse they can more cubes are multiplied into one it may be possible to bring them closer may be 10 or 20 anyway if it works for u let me know afterall its a year or maybe 2 now cheers

@venkatbabu186 5 лет назад

You take two cubes and add an edge you have three surfaces. The switch between multiverse.

@venkybabu8140 2 года назад

17 odds. 12+5. 3+2. Inversion. Elon Musk. √5 -1. Usually 0.6 is inversion and 1.6 extention. That's why most square equations have two roots. When you are finding roots it is the curvature of space or line.

@reuvengad9148 6 месяцев назад

Dr. Holly Krieger 💙 🇪🇸

@Mjr._Kong 6 лет назад

I'm in exponential love....

@00BillyTorontoBill 6 лет назад

Is that Grimes house?

@AaronHollander314 6 лет назад

And why doesn't he hang those frames?

@ernestboston7707 5 лет назад

It is more fun to write the equation as 3^2-2^3=1^23

@petterhouting7484 5 лет назад

Or 3^2-2^3=3-2

@ernestboston7707 5 лет назад

Dale Kerr Quite eXcellent !!!

@pablozumaran3997 5 лет назад

Do you mean 3²-2³=1²³? :D

@MatBaconMC 5 лет назад

@@pablozumaran3997 HOW

@pablozumaran3997 5 лет назад

@@MatBaconMC Key combinations: AltGr+2, AlgGr+3.

@Adraria8 6 лет назад

My 9th grade math teacher called perfect powers “sexy numbers”

@imagination7710 6 лет назад

Sounds inappropriate tbh

@thesmart4128 5 лет назад

@Diego Maradonna although those would be called sexy primes

@becamicusack3598 5 лет назад

@@nexusclarum8000 You sound pointless tbh

@iamnickyj 4 года назад

My 9th grade math teacher called me Nick-mobile, then I found out he called Steve, Steve-mobile. I was devastated, though I was special, guess not

@justinsalvatierra5476 4 года назад

As they should be

@zeezozeezee7482 6 лет назад

when you’re single and have to watch math videos

@LuckyTondi 6 лет назад

WANT and CHOOSE, not "have to", pffff

@kranklg2s 6 лет назад

Dont worry. I'm engaged and I'm still watching math (and some history) videos. ^^ Math loves you!

@sharofs.6576 6 лет назад

and you don't even study mathematics

@ilprincipe8094 6 лет назад

XSimoniX so true bro

@alphascooper7797 6 лет назад

😂

@eduardomuller9973 6 лет назад

OMG a new conjecture of math! "This conjecture was already proven" WHY DON'T CHANGE IT TO A THEOREM????

@jchry3688 6 лет назад

Eduardo Muller It's been proven by Mihailescu You can legally call it Mihailescu's Theorem

@abdulmuhaimin9780 6 лет назад

Alliteration. The only reason

@peterjohannsen2183 6 лет назад

I would think that it is because it's probably an old conjecture, so people are just used to calling it and referring to it as a conjecture?

@clickaccept 6 лет назад

It was Catalan's Conjecture. There is no inconsistency in this terminology.

@smitashripad9757 6 лет назад

Just to sound very very very very very very tough

@sebastianelytron8450 6 лет назад

Catalan's Conjecture is too strong a theory and wants to separate from the rest of mathematics. It wants to be in its own independent set. Can't blame it.

@50mt 6 лет назад

[Catalonia joke]

@user-wu7ug4ly3v 6 лет назад

There is nothing in the mathematics constitution that allows this conjecture to separate itself.

@bitterlemonboy 6 лет назад

lol catalonia

@livedandletdie 6 лет назад

Asturias> Catalonia > rest of Spain > rest of Arab blood filled nations.

@grecolonsvila 6 лет назад

Damn your racism is over 9000. Get back to your mine.

@johndue2366 6 лет назад

For an elder (+60), average electronic engineer with a major interest in math, this channel is awesome.

@marios1861 4 года назад

I'm currently studying electrical and computer engineering. Has your job been fulfilling?

@jonnamechange6854 4 года назад

Yeah, of course it has. He's so full he can't even move.

@amanjain1701 4 года назад

I know its you electroboom @electroboom

@YorukaValorant 4 года назад

I'm 21, Been Watching since 17 :D

@RetroGamingClashOfClans 4 года назад

uh, you make me feel old.. im just 17

@feuernarr8330 6 лет назад

In my first semester at the Georg-August university in Göttingen (Germany) the linear algebra lecture was given by Preda Mihailescu. Nice to hear his name in one of our videos!

@SciencewithKatie 6 лет назад

That's awesome!

@sorinichim4737 4 года назад

My conational😎

@TheMrbaummann 2 года назад

That course is still infamous at Göttingen uni as the "linear algebra course which almost nobody passed" :D

@Brien831 2 года назад

@@TheMrbaummann I passed it in 2019! Preda is totally awesome

@wolframhuttermann7519 Год назад

Göttingen needed such a mathematician after Hilbert, Dirichlez and Gauss.

@johnchessant3012 6 лет назад

26 is the only number that simultaneously is one more than a square and one less than a cube.

@maxilexow 6 лет назад

Can you prove it?

@johnchessant3012 6 лет назад

Maxi Lexow Yes, it uses unique factorization in Z[sqrt(-2)].

@nazishahmad1337 6 лет назад

now its known as john cessant conjecture

@sieevansetiawan4792 6 лет назад

This problem currently appears in brilliant advanced weekly problem.

@caffreys1979 5 лет назад

Yes so is a unique soln to x^2 + 1 = y^3 - 1. (x,y) = (5,3)

@liweicai2796 2 года назад

2:56 I'm kinda surprised that this was proved algebraically. Most difficult number theory problems seem to be tackled analytically nowadays.

@gytoser801 2 года назад

If you look closer it's about groups, space and abstract algebra. How would you prove otherwise

@guitarraccoon1541 6 лет назад

when you're sitting alone on Valentine's day and numberphile makes a new video. Thank you numberphile, atleast you give me math.

@SciencewithKatie 6 лет назад

😂👏🏼

@superchet4026 2 года назад

And Holly.

@aviraljanveja5155 6 лет назад

This Conjecture was proven by Preda Mihăilescu, at the University of Paderborn ! Honored to be able study at the university in 1 month's time ! XD

@goldminer754 3 года назад

He is teaching now in Göttingen, you would have even had him in linalg 1&2 and algebra if you started 2 years ago in Göttingen.

@WolfgangGalilei 3 года назад

so how did it go? hopefully you learned a thing or two!

@hexisplus9104 3 года назад

I love paderborn

@Brien831 2 года назад

@@goldminer754 I had him in my AGLA1 course. He is a really cool guy, his lecture is a bit all over the place though. Proving the fundamental theorem of Algebra to first semesters the Gauss way isnt really cool. Möbius transformations arent nice either for 1st semester students!

@liviu445 2 года назад

Let's go romania.

@ffggddss 3 года назад

Of course, there's always a next question(s), once something like this gets settled. Like, is there a point beyond which there are no more differences as small as d, where d is 2 or 3 or ... For instance, are 25 and 27 the last pair of powers that differ by 2? Are 125 and 128 the last pair that differ by 3? Are 2187 and 2197 the last pair of powers that differ by 10? Etc. Thanks! This was fun!! Fred PS. A reply 2 years ago, by dlevi67, to a similar comment of mine, points out that, "Pillai's conjecture says that there are only finitely many misses for any integer value of the miss."

@JMUDoc 2 месяца назад

"For instance, are 25 and 27 the last pair of powers that differ by 2?" Fermat (_that_ Fermat) did prove that 25 and 27 are the only _square and cube_ that differ by two, but that's a very small bite out of the question!

@noohairdontcare 6 лет назад

I don’t “crush on” RU-vid celebs but omg I think I’m in love.

@BobStein 6 лет назад

I've never found any category of people to be categorically excluded from crush potential. Patterns of people are about as useful as patterns in clouds.

@pumajlr 6 лет назад

Bob Stein He's propably saying that he's not a tennager who loves somebody just because he like the videos they make. The "pattern" can inform about the people he like or why he likes them. And patterns of people are totally useful. We classify people all the time because of that.

@PS3RatBag98 6 лет назад

Bob Stein What about Trump supporters?

@Marco9603 6 лет назад

I have a thing for women that show a passion and enthusiasm for something!

@itsJPhere 6 лет назад

I could listen to Holly explaining anything all day and not mind at all, some people have that special something.

@lookbacktime9422 6 лет назад

Thumbs up for the Romanian mathematician !!!

@sharoneisenberg2274 5 лет назад

I thought he was Catalan...

@instakilogram3230 5 лет назад

A noastră!!

@borgirvspitsah7329 5 лет назад

@@sharoneisenberg2274 the mathematician who proved the conjecture is Romanian

@PercivalBlakeney 4 года назад

@LookBackTime Nice to have a famous Romanian other than Count Dracula. I'll get my coat.

@stv3qbhxjnmmqbw835 4 года назад

Theoretically, vampires are intelligent beings

@madlad255 4 года назад

2:50 Wait, that's a French poem, not math!

@sharkinahat 6 лет назад

Of course you got Dr Krieger for valentines... I ain't even mad tho.

@lb5sh 6 лет назад

She's intelligent and incredibly charming. What a perfect combo.

@UnimatrixOne 5 лет назад

😍

@paologalli5803 5 лет назад

beautiful beautiful

@vinayvardhanyt2415 4 года назад

Beauty with brains

@Taricus 5 лет назад

2:50 what does that French literature have to do with the math? LOL! It's pretty, but.... XD Kinda random....

@madlad255 4 года назад

Yeah, I noticed it too, I'm not going to even try translating it... Or I guess I could move it in the plane. That's also translating ;)

@pedroespino6988 4 года назад

I've got the feeling that, all of a sudden, a lot of people are going to become very interested in maths.

@Ragwar 6 лет назад

Preda Mihāilescu.........what!?I can't believe that a romanian made it to numberphile I am so proud 🇷🇴🇲🇩🇷🇴

@JonSebastianF 6 лет назад

Isn't that the *CGP Grey logo* standing in the corner? :D

@daggawagga 6 лет назад

that's a funny way to call it!

@MrDannyDetail 6 лет назад

I think it is. Perhaps it's subliminal cross-promotion.

@danthebat666 6 лет назад

It's the Nail and Gear! Flag of the Hello Internet podcast.

@DoctorWhom 6 лет назад

"CGP Grey" is a funny way to spell "hello internet"

@pepegapig1489 6 лет назад

Dr Holly Krieger😍😍😍😍

@jackthmp 6 лет назад

claiming Hannah Fry

@calebhein8043 6 лет назад

RIGHT?!?

@Q_QQ_Q 5 лет назад

*Dr Holly Krieger is so white and redhead that i need my dark glasses to even see* . 😂😂😂😂😂😂😂😂😂😂😂😂

@redaabakhti768 4 года назад

This boss level beauty

@CaptainSpock1701 4 года назад

3:09 - "We don't have time for the next 'couple of years'..." - *Looks at watch* - I thought that was very funny.

@sam_kant 6 лет назад

Came for the mathematics, stayed for the mathematician.

@nymalous3428 6 лет назад

I do love that moment of clarity and understanding when learning something new (...I also enjoy watching someone else experience it when I am the one teaching). Most of the math in these videos goes over my head, but I always seem to get just enough to get a brief moment of learning. Thanks again for doing these videos!

@abcdefvxyz4324 6 лет назад

thumbs up for the romanian mathematician

@hexagon-77 6 лет назад

Are you Romanian?

@abcdefvxyz4324 6 лет назад

yes

@mashmax98 6 лет назад

Preda Mihăilescu for President, he's currently hibilitated in göttingen, Germany which is where i am studying

@lorinczadrienjeno4839 6 лет назад

Sal fra

@tianyima8642 6 лет назад

My fav math prof is Romanian! And one of my fav ow players. Start to develop a strange fondness for Romanian people :p

@Yetiforce 6 лет назад

Dr. Holly Krieger is perfect for a Valentine's Day Numberphile!

@lincolnsand5127 6 лет назад

You're a weirdo.

@Vextrove 5 лет назад

What

@V-for-Vendetta01 4 года назад

@@lincolnsand5127 lol

@OlafDoschke 6 лет назад

There are infinite powers with difference 0, though.

@OlafDoschke 6 лет назад

Yes, with whole numbers, too.

@tonydai782 6 лет назад

Because all powers of powers have a difference of 0 to the base of the power of the power, to the power of the product of the exponents so you can have infinite examples of this

@mashmax98 6 лет назад

2^2n - 4^n

@dlevi67 6 лет назад

Even simpler: n = n (each number, no matter if a perfect power or not, has difference 0 to itself)

@OlafDoschke 6 лет назад

n^1 is excluded, as far as I see. If these numbers are in, well, you had infinitely many gaps of difference 1... So that's too simple, I am talking of 2or more representations of the same number. Not all numbers have that, eg 2^2 is the only perfect power (of integers) resulting in 4, but still there are infinite numbers with 2 (or more) perfect powers and thus a difference of 0 between them. That's just not asked for.

@JMUDoc 3 года назад

If "for any n, there exist perfect powers differing by n" hasn't already been conjectured, I demand that it be named after me.

@ferociousfeind8538 3 года назад

Ah, the Jay-Mu-Doc conjecture I feel like the larger n is, the more examples of perfect powers differ exactly by n. The problem, in the form of "a^b - c^d = n" is far too free to have any integer n that doesn't also have at least one set of integers a, b, c, and d

@zacharychase7652 3 года назад

I think it's conjectured that there are no two perfect powers differing by 6.

@steveyankou4144 6 лет назад

Have you considered changing the name of the channel to "numberwang?"

@zyaicob 4 года назад

m a t h p e n i s

@aakksshhaayy 5 лет назад

Two plus two is four minus one that's three. Quick maffs

@prestonhall5171 5 лет назад

Congrats

@hectooooor 5 лет назад

Old but kinda gold

@1234s6 5 лет назад

(x+1)(x-1)=y^3 Hey can anyone explain why BOTH have to be cubes and not just one?

@jungunddumm8023 5 лет назад

Get a book on number theory

@adamhrankowski1298 5 лет назад

The two factors differ by exactly two. We are assuming that y is odd. Since the differ by 2, they can have no common factor. We need 3 copies of each of the factors of y, because y is cubed. These three factors are distributed between the two factors x-1 and x+1. But since those two factors don't share any factors between then, a given triplet of y factors has to be assigned to either of x-1 or x+1. Hence, they are each cubes.

@ralfoide 5 лет назад

@@jungunddumm8023 That was rude and unhelpful. Always encourage someone who wants to learn.

@dbliss314 5 лет назад

The factors are the same on both sides of the equation. If (x+1) had a non-cubed factor, and (x-1) did not have that same factor at all, then y^3 must also have that non-cubed factor. y^3 cannot have any non-cubed factors, because y^3 is a perfect cube. Therefore (x+1) must only have cubed factors. Therefore, (x+1) must be a perfect cube. Ditto for (x-1)

@pythontron8710 4 года назад

Jung und Dumm last name checks out

@andrewcgs 6 лет назад

I love Numberphile videos featuring Dr Krieger! ...Happy Valentine's Day y'all, I guess?

@AlabasterClay 6 лет назад

That was really fun. I think it is nice to go ahead and start down the right path....even if we can't follow the whole big proof. Thanks!

@TheOriginalNCDV 6 лет назад

This has to be the most distracting Numberphile video I've watched.

@uruiamnot 6 лет назад

Just picture an old, crusty professor in a suit and tie, with his back turned, stammering at a blackboard in a damp, drafty lecture hall with poor lighting. And needing a shave. And a throat lozenge.

@travellcriner6849 6 лет назад

but wait... WHICH ONE OF US NEEDS THE SHAVE?!!?

@Arycke 6 лет назад

The one with Hannah is moreso ;) then again, just an opinion as beauty is subjective. They are both intelligent and attractive.

@harryv7877 6 лет назад

How come?

@reissner1967 5 лет назад

ncdv47 I'll second that! o/

@wolframhuttermann7519 Год назад

I know the mathematician who proved Catalan conjecture. Prof Mihailescu did it in 2004 and gives lectures in Göttingen where I used to study math.

@phscience797 6 лет назад

What I think is even more interesting about those numbers is: Is every natural number a difference between two of those Catalan numbers?

@jpdemer5 2 года назад

Nobody's proved it for the number 6, let alone "every natural number." Or for 14, or 32, or 42, or 50... there's an apparently infinite number of (conjectured) counter-examples (A074981 in the OEIS)

@juancarlosortiz6756 2 месяца назад

I remember hearing one time a conjecture similar to Catalan's; namely, the only (positive Diophantine) solution to x^a-y^b=2 is 3^3-5^2. In other words, 26 is the only positive integer that is "sandwiched" between two perfect powers (25 and 27). Does anyone know if this conjecture has a name, or if it has been proven?

@lilyfox2981 6 лет назад

I’m watching because numbers are actually dependable-unlike a relationship. 😂😅😓😞

@dlevi67 6 лет назад

Oh, I don't know about that. How much is 1 + 2 + 3 + 4 + ...?

@skmelbo 6 лет назад

The sum diverges towards positive infinity.

@dlevi67 6 лет назад

And you call that dependable? Divergence, infinity? Mysterious rational asymptotic coefficients of -1/12 in a sum of positive integers? (I'm joking - as I was joking above)

@LeeOades 4 года назад

I've found some numbers to be quite irrational...

@朕是神 4 года назад

The conjecture was x^a-y^b=1 has only one solution, not x^2-y^3=1 only has one solution. How is this proof?

@ffggddss 6 лет назад

An interesting observation I've often wondered about, but had no idea was actually being tackled by mathematicians! There are a number of other "pretty-close" cases. 5³ - 11² = 125 - 121 = 4 · · · ↓ 2⁷ - 5³ = 128 - 125 = 3 . . → these two examples are all the more interesting, because there are *three* powers within a short span (7) 13³ - 3⁷ = 2197 - 2187 = 10

@dlevi67 6 лет назад

Pillai's conjecture says that there are only finitely many misses for any integer value of the miss.

@timgillam7964 Год назад

And 2209 = 47^2 comes shortly after 2187 and 2197 too, so there's another bunched up trio of powers

@ajeyavaani1366 2 года назад

can someone please tell me how she came to the conclusion that (x-1) and (x+1) both have to be cubes?

@meirihagever9132 4 года назад

*"Yeah that's exactly right"*

@giantbluefish2859 4 года назад

But like... what about 1^2-0^3

@myrus5722 6 лет назад

I literally typed in “that conjecture where there are only two palindromic powers and they do some things”.

@mayukhpurkayastha2649 3 года назад

Sir i m invent tree sensorable Ai algorithm or tree sensor computer system and power acceptor large machine. This power acceptor help update new type quantum computer Bihar Bihar India

@UnSimpluJucator 6 лет назад

OMG a fellow romanian demonstrated this? Nice one.

@blueghost3649 5 лет назад

Yes, a Romanian

@kurzackd 5 лет назад

5:10 -- that wasn't explained well at all. Why should it follow that both x-1 and x+1 are cubes, if either at all???

@ralfoide 5 лет назад

Replied 1 month ago by Adam Hrankowski: "The two factors differ by exactly two. We are assuming that y is odd. Since the differ by 2, they can have no common factor. We need 3 copies of each of the factors of y, because y is cubed. These three factors are distributed between the two factors x-1 and x+1. But since those two factors don't share any factors between then, a given triplet of y factors has to be assigned to either of x-1 or x+1. Hence, they are each cubes."

@guepardiez 2 года назад

Since it is proven, can we please call it Catalan's theorem instead?

@24ever66 4 года назад

Bringing Holly in was the best thing numberphile has ever done

@harryhirsch3637 2 года назад

That's not fair to Hannah Fry!

@jettzheng2791 2 года назад

The ambitious juice preferentially invent because toilet lastly clap apropos a deeply beauty. descriptive, dirty poppy

@Jamie720p 6 лет назад

I spy a mighty Nail and Gear

@daggawagga 6 лет назад

No Saturn rocket box in background :(

@NischalKK 5 лет назад

I'm a year late but I needed to jump in the comments to say this.

@ronmasters751 3 года назад

Happened to see this on my 72nd = 3^2 x 2^3 nd birthday, having been born on 3 primes: 7/17/1949. 🎉

@MultiHanspeterwurst 6 лет назад

here I am, laying in my bed watching youtube videos, not learning for my exam tomorrow and there is a video about one of my professors at the university of Göttingen 😂

@fabiorota9661 3 года назад

This was a very bad explanation

@Afdch 6 лет назад

Oooh, a public service broadcasting's race for space! A great album.

@mackycabangon8945 6 лет назад

EVERY FREAKING TIME I look at the title I think of Catalonia

@vinayakchawla2510 3 года назад

Why will both the factors be cubes?

@JianJiaHe 5 лет назад

1^0-0^2=1, no thanks!

@brace5138 5 лет назад

So apparently this is the first time this comment section has ever seen a female.

@Peter_1986 5 лет назад

+you toob You would see the exactly same comments from girls if the person in the video was a very attractive man.

@1missing 6 лет назад

That entire explanation after "if y is odd" made zero sense to me

@_x_asgard5_x_861 5 лет назад

People aren't supposed to understand math

@druid_zephyrus 6 лет назад

Why not x=1 and y=0....1^2-0^3=1 does it not?

@richardfarrer5616 5 лет назад

Typically the answers are limited to natural numbers starting from 1. In integers, you are correct, however, and there's also (-1, 0) and (-3,2) as answers.

@missquprison 6 лет назад

"8 is too cute" indeed it is :D

@trueopsimath 4 года назад

How to describe Dr. Holly Krieger? Imagine a cheerleader with an IQ of 150

@thepsychocybe7078 3 года назад

math momy giv me milkies

@javiercorral7820 4 года назад

I've been puzzled by 2 cubes in geometry in recent time, would you provide me with your interpretation, please?

@nicolallias 6 лет назад

Why does the video's description does not tell anything about the video subject? Not even the name of Mihăilescu?

@JankieHands 6 лет назад

Watching this from catalonia

@neelparmar6690 6 лет назад

Jankie Hands do you know if the guy named Catalan was actually a Catalan?

@jaumecasanova551 6 лет назад

I per què es diu catalan?

@epsilonalpha2430 6 лет назад

You mean Spain

@BobStein 6 лет назад

You're watching a video about perfect powers *separated* by one? (Sorry, couldn't resist.)

@jaumecasanova551 6 лет назад

Bob Stein Hahahaha separation yeah... Not as power in spain :)

@douglaslarson532 5 лет назад

You lost me when you said "both (X + 1) and (X - 1) have to be cubes". Why do they have to be cubes?

@wurnotantmlb 5 лет назад

so really charmming!!

@svendsoemod 3 года назад

Made a little python program to calculate perfect powers [1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400, 441, 484]

@habibikante9472 3 года назад

hey thats amazing ! can you send me the program?

@svendsoemod 3 года назад

@@habibikante9472 Thanks, I think i just deleted it when it was done

@brawnstein 6 лет назад

0^a + 1^b = 1

@tungstentoaster 2 года назад

In my mind, the most natural way to show that x^2-y^3=1 only has the one known solution would be putting x^2 and y^3 on the same axis of a graph and showing that they diverge after x=3; y=2.

@smurfyday 2 года назад

If you figure out a way to graph to (not towards) infinity, let us know.

@ruiningwang1644 6 лет назад

Il y avait un jardin qu'on appelait la Terre, Avec un lit de mousse pour y faire l'amour. Erm... Happy Valentine's day I guess??

@plop0000 6 лет назад

I am pretty sure it is a poem about puberty....

@markmayonnaise1163 6 лет назад

Est-ce qu'on fait ça à c't'heure ? Va-t-on y laisser les poèmes ?

@antimatter2417 6 лет назад

On écrit Terre avec une majuscule et deux r, l'ahuri

@Cycliberte 6 лет назад

Anti Matter pas de majuscule dans le poème en tout cas!

@ruiningwang1644 6 лет назад

Anti Matter Hep! Merci l'éberlué!

@gormster 6 лет назад

I usually find numberphiles easy to follow but I didn’t get this one at all… why does exactly one of those two have to divide y? That’s not the only way of factorising x² - 1..

@hlb4590 6 лет назад

if (x+1) and (x-1) have a common factor p thus x+1=ap and x-1=bp with a>b. Moreover p(a-b)=2. y is odd thus p>2. Hence 2/(a-b)>2 thus b>a. that is in contradiction.

@maxlepocher2627 6 лет назад

herve your last inequality should read " b>a-1 " , after some thought the contradiction still exists .

@mrmaxi118 6 лет назад

Where is numberphile live from maths fest?

@Rearmostbean 6 лет назад

I regret clicking this

@ThePharphis 6 лет назад

Great video. Hopefully you'll do more proofs with Holly

@summertilling 3 года назад

I like how the thumbnail suggests that it's conjectured that 9-8=1, but that no-one can quite prove it.

@mathsmoica 6 лет назад

*Studying conjectures is my passion.*

@BobStein 6 лет назад

I conjecture you have yet to find your life's most interesting conjecture. (Unless that was it. But then it was still true when I conjectured it.)

@ErdTirdMans 2 года назад

Please do more with Holly!

@theultimatereductionist7592 6 лет назад

Stop calling it Catalan's conjecture. It's been Mihăilescu's theorem since 2002.

@vivvpprof 5 лет назад

I suppose, if it had been a Briton, or a German at least, it would've been long renamed... Shame.

@almanahulzilnicdesuceava5379 6 лет назад

It.s ROUMANIAN and we did not know about him!

@UnSimpluJucator 6 лет назад

Ikr

@stumbling 6 лет назад

Shouldn't this be Mihailescu's Theorem then?

@waynewelshans1172 5 лет назад

Dr. Krieger, you are a true unicorn :)

@davetoms1 6 лет назад

5:29 Incorrect. We have two examples, not one example, of two cubes differing by two: (+1),(-1) and (8),(9). Unless you assume x cannot equal zero, (x-1)(x+1)=y^3 resolves for both (x=0,y=1) and (x=3,y=2).

@thomasgarrett1828 6 лет назад

Very interesting problem. Happy Valentine's Day!

@trevortucker9586 2 года назад

I like how I failed every single aspect of math throughout many years of schooling and yet somehow by watching this video I naively thought "oh hey, you're older now Trevor, you'll probably understand what's being said"