How To Find The Inverse of a Number ( mod n ) - Inverses of Modular Arithmetic - Example

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This tutorial shows how to find the inverse of a number when dealing with a modulus. When dealing with modular arithmetic, numbers can only be represented as integers ranging from 0 to ( the modulus minus 1 ). This tutorial shows one method that can be used when solving for an inverse of modular arithmetic.
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Опубликовано:

25 сен 2013

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Комментарии : 247

@trollerxoxox 7 лет назад

Thank you for explaining it so well. I hate it when some other mathematicians just show off by being cryptic, its so frustrating. Your tutorial was a tiny tad slower but made it so much easier to follow and learn. Thanks.

@nahiyanalamgir7056 Год назад

The thing is that mathematicians use symbolic representations and formulas to summarize stuff in a compact way - but that's terrible for explanation. They should refrain from doing that and instead explain things in a human-friendly way!

@logisec Год назад

@@nahiyanalamgir7056 Suffering from this right now in my Cryptography class, absolutely soul-sucking explanations in this class

@KitKatSam27 5 лет назад

This was amazing. Way better step by step explanation than my professor. THANK YOU!!

@sharvesh0369 Месяц назад

Been searching all night for this to learn chinese remainder theorem for tomorrows network security exam. This one is a LIFESAVER

@c0wqu3u31at3r 8 лет назад

Can I just say thank you on behalf of everyone at QMUL taking the Algorithms and Complexity module. This has really come in useful with trying to understand RSA encryption!

@mathhacker4764 6 месяцев назад

Same, had to learn this topic to understand RSA encryption!

@kingkevthebest3114 Месяц назад

man rsa encryption is 8th grade math

@kaylaburrell4637 5 лет назад

This makes sense now! I decrypted an affine cipher, but afterwards, I couldn’t figure out how I got -5 as the inverse of 5 or how it worked. After watching this video, I worked it out and got -5 again. Apparently, I’m just the type of person to use actual math successfully by accident.

@learnmathtutorials 10 лет назад

If that is the case, I would guess that you simplified a little early. When doing this process, it is important to leave terms as multiples of two numbers, so that one of the numbers can be replaced by an equation above. I hope that helps. :)

@iamriotus 8 лет назад

Absolutely amazing tutorial! Preparing for my exam, I couldn't find a good explanation anywhere! You really saved my bacon!

@MAGonzzManifesto 10 лет назад

Thank you so much! I feel confident doing these kinds of problems now!

@sethmarcus1784 5 лет назад

Excellent video clearly demonstrating how to calculate the inverse of a number(mod n). Very grateful for this video!

@CatherineWeeks 2 месяца назад

Thank you so much for this! I have a discrete final coming up and it's the videos on niche topics like this that are really getting me through. You teach it so well too, thank you so much for putting your effort and time into videos like these.

@bensosfrequents 9 лет назад

doing Bsc mathematics and computer science in pure maths section (number theory).... this tutorial has really really improved me.... i have not only understood linear congruence but also cryptology... nice and God bless you

@nadianoormohamed4432 7 лет назад

great video!!!!! You explain it in a structured way which is essential for a topic as such. Thanks!

@ajk7151 5 лет назад

awesome explanation! looking forward to check out the rest of the videos. :)

@richardwalters9249 6 лет назад

This is a great instructional video ... I still need to clean up some details in my understanding ... but this question: Is there a check you can do to verify the answer ? I’m trying to do 27^-1 (mod 292) compared to 363 ( mod 392) ... or, am I thinking about this wrong ?

@anmaraljanabi7137 7 лет назад

Thanks you very much sir, wish you continues success

@sillupiiks 6 лет назад

Thank You so much! I spent an hour with my teacher today and I think now I finally got the idea:)

@fairlymoon448 7 лет назад

hey any chance you can make a playlist of these so we know which order to go it? just watched the positive mod change vid and im pretty sure next should be the negative mod but its this? which i dont think should be next?

@Robertlavigne1 8 лет назад

THANK-YOU!!! So intuitive when shown this way. My proff skipped a bunch of steps and it went right over my head. Much appreciated!

@MultiDman2011 Год назад

Thank you so much for making this understandable and easy to follow. Life saver!!

@RobinsonGames 5 лет назад

This really helped a lot. Feeling much more prepared for my exam now

@swizinSims 3 года назад

Thanks so much THIS IS EXACTLY WHAT WAS MISSING IN OTHER VIDEOS MUCH APPRECIATION!!!!

@TheGamerViewer 6 лет назад

Thank you so much! best guy on youtube for this tutorial!

@amandaniess7028 6 лет назад

Thank God! I have an exam tomorrow and I've never really understood how to use the algorithm to find aninverse. I like u.

@amarachiukor4016 2 года назад

Your explanations on this topic is so on point. Thanks alot

@bernie8571 10 лет назад

wow thank you for making this. it helped a ton!

@ibejoseph19 Год назад

I've been looking for a video like this for weeks. After another seemingly fruitless search, I prayed and just stumbled on your well explanatory video. Thank you very much.

@rasberybanana 8 лет назад

very helpful video, are the equal signs at the end supposed to be congruence signs?

@ethansimmons82 4 года назад

I should've found this video first! It was very clear, thank you.

@arefinahammed8408 3 месяца назад

after 10 years. Thank you. Was going crazy :')

@evermoregwatiwa8001 4 года назад

this is the best explanation ever. thumps up man.

@atomic_godz 9 лет назад

Just what I needed, thanks a lot man

@declanallan885 7 лет назад

awesome video dude, love how you used the different colour schemes to segregrate some of the concepts behind what was going on!

@JPfromDport 8 лет назад

Great video, helped me understand how to deal with negative numbers in Bezout's theorem.

@p1q2r 4 года назад

The best explanation for modular multiplicative inverse.. Thanks much!

@greatgymdj 10 лет назад

Very nice video, my lecturer just expected us to guess how to do this! Thanks :)

@bharathraj1646 3 года назад

Thanks a lot , it was very helpful. Could you please make more videos on modular arithmetic algorithms . It would really help me a lot. Thanks once again :)

@JohnSmith-kf1lq 10 лет назад

Very helpful. Thanks for making

@danielbuckley9651 6 лет назад

Very nice video, good use of colours. Excellent explanation of the Euclidean algorithm leaving no steps out. Well done.

@savantdude 4 года назад

amazing explanation! saved me a lot of time!

@Arkansas28 2 года назад

Excellent, thanks for the video.

@CSBIBLE21 4 года назад

this was very good, exactly what i was looking for

@HypnotizeCampPosse 10 лет назад

Learn Math Tutorials I like how you solved for the remainder values first in the video, then went and did the Reverse Eulcidean Algo (REA) This method is different from every other method I have seen demonstrated (where they do the REA and computer the replacement values on-the-fly). I think you way will keep me organized better, thanks for making the video.

@blacklotus5953 5 лет назад

Great explanation! Way better than my lecture at uni

@josephcario2659 8 лет назад

boss tnx now I can explain it very well to my students.there are lots of video related to this bt this clearly explains the topic.nice...

@vestigialSmile 5 лет назад

Thanks man! Came in handy with Abstract Algebra

@mahendrakotapati9970 5 лет назад

you had explained in very clear manner thanks sir...

@AndrewBaba 9 лет назад

The best explanation on the youtube I found so far. Thank you

@EsteBandido_YT 5 лет назад

question, and a really big one. by the equal sign, you mean the congruence, correct?

@Tuzkichen 6 лет назад

very clear explanation, thanks!

@PhamQuang 4 года назад

Having an exam coming next week. You saved me. HUGE THANKS

@chnoco 6 лет назад

Thank you so much this is so useful great job!

@zetsubou-chan 2 года назад

Thank you for a great explanation!

@unminified 10 лет назад

Hello I was wondering what kind of program do you use for all of your videos to write on the computer? Thanks

@omberry7950 Год назад

very very thanks.. i am strugling with inverse. you solved the problem very efficiently .......

@feysalimran 7 лет назад

Pretty nice tutorial, even after all these years. Sir am wondering, if we had had a positive number instead of a negative one at + 27(-29)...., would we have still subtracted it from 392 or added it instead?

@alial-musawi9898 6 лет назад

Feysal Imraan 27 (mod n > 27) = 27 So you leave the 27 as is.

@TaylorCaRRtel 9 лет назад

Studying for my final and couldn't figure this out for the life of me. Your explanation was great. Thank you

@AndrewT34pot 8 месяцев назад

thank you, well explained video

@coldair0010 10 лет назад

what if i am left with a constant on the left at the end

@BGSoccerMagic 9 лет назад

Can someone explain to me what's the practical use of modular arithmetic if we don't count encryption which is used automatically and with a very large numbers?

@shaheershakeel6851 2 года назад

Thank you! This was the best explanation of EA and EEA I've been through. I still have no idea why tf this thing exists though

@darrenmau1942 9 лет назад

Well explain, good example, thank you very much that helps so much

@hafilahmustaffa 3 года назад

thank you so much. I spend a day to find the solution for d equal to negative. Superb.

@logankoester2845 9 лет назад

In the step where you calculated 363 by subtracting 29 from 392 (392-29=363) does the negative come from the -29? So if 29 were positive would you add 29 to 392?

@waltvanamstel6807 9 лет назад

Logan Koester He found the answer to be -29. That is a valid answer, but you will often be asked to find the positive inverse. -29 and 363 are essentially the same number under mod 392.

@kingsleyobi7482 4 года назад

Wonderful tutorial!!

@user-tv7vo2jd1q 2 года назад

Thanks you!! it is really helpful for me to understand.

@adangonzales8085 10 лет назад

5 Star rating for this video!

@shubhamchaudhari790 10 лет назад

r u mad ..... :P :P

@vash47 9 лет назад

Thank you so much, mate.

@learnmathtutorials 10 лет назад

Thank you. Not every number in a mod field will necessarily have an inverse. For example 2 (mod 4) does not have and inverse since 2*0 = 0 (mod 4) .... 2*1 = 2 (mod 4) ... 2*2 = 0 (mod 4) ...2*3 = 2 (mod 4) ... none of these results produce 1 (mod 4) and you have checked 2*0 , 2*1 ,..., 2*(n-2) , 2*(n-1) where n is the mod.

@aadilmufti4933 5 лет назад

Great explanation!

@santiagowhite5467 4 года назад

So easy to understand ty

@NandaAcademies 3 года назад

Excellent explanation which is useful in understanding RSA algorithm.

@danielmartino8068 3 года назад

Thank you for the explanation, you say me a lot of theory

@rinzinnorbu3518 5 лет назад

very good expatiation thank you

@CptGankbawlz 10 лет назад

Thank you so much! While reading my book I was completely lost! You made this so simple to follow and understand. Thanks again!

@christanjhayyap2015 3 года назад

This is very helpful

@phnml8440 2 года назад

Is my thinking correct that you can only find an inverse if the gcd(a,n) = 1 where a = 1 (mod n)

@billyandej 3 года назад

I hope you’ll answer this question right away. Badly needed. We’re going to report this topic this coming Thursday. May I know why do we need to get the multiplicative inverse of the given? just like in the example. Why do we need to get the inverse of 27 (mod 392) and it should be congruent to 1 mod 392?

@mathhacker4764 6 месяцев назад

Thanks sooooo much.

@lilmonkianime8084 4 года назад

What should I do , if there is natural number in the givens, not number with -1 degree?

@CALLm151 4 года назад

How to calculate 1/a mod m using only these operations: a^b mod m, a*b mod m, a+b mod m, a-b mod m ?

@akamfoad 3 года назад

great thanks for the explanation!

@shushmitam.s7884 6 лет назад

Great tutorial! :)

@apondikevinomondi5003 7 лет назад

You rock. Thanks a lot

@SomeOne-el9mr 5 лет назад

Thanks. You helped me alot

@totasalam7060 9 лет назад

thank you sooo much .. u r the best

@medadrufus 8 лет назад

Thanks this is awesome!

@programjm 2 года назад

What happens when the number and n are not coprime? I.e. the GCD is not 1. Would we have to divide by the gcd?

@VaibhavNaik26 9 месяцев назад

is there an easier way? to find x? or the inverse of mod? please let me know

@hilufabebe4721 2 года назад

best explanation

@umeshstudypoint7495 3 года назад

Very helpful

@louisaldorio7251 4 года назад

what if the place where 27 is changed to be larger than 392? is this still possible?

@rapidreaders7741 5 лет назад

How would you take the inverse of 2 (or any other even number) in mod 392?

@patogenny 5 лет назад

2 (or any other even number) don't have inverse in mod 392 (or any other even number). If x would be a inverse then 2*x= y*392 + 1. 2*x must be even and y*392+1 must be odd.

@abhijithbalan5107 3 года назад

Thanks a Lot Sir

@ZeeshanAhmad-xt4pi 6 лет назад

so nice explanation .

@shivanineharkar2571 Год назад

Dude you have helped alot😇😇😇😇😇😇😇

@clarissasuhanda7983 10 лет назад

I calculate 1/27 mod 392 with matlab, and the result is 1/27. Why is it different? Thx..

@janarddansarkar3447 6 лет назад

what if we have to calculate inverse of a negative number?

@thelazyfrog9520 9 лет назад

Sir. It was a brilliant tutorial ... Just wondering if I have learnt this well or not. Is 7 inverse mod 31 = 9 ? Please advice.

@learnmathtutorials 9 лет назад

Debajyoti Biswas Yes! Good Job! :)

@marksahlgreen9584 6 лет назад

I am sitting with this exact same calculation, and I can't make it to be 9 >_

@Haragavi 5 лет назад

Yeah bro. I've also go it :)

@bawarkhalid2651 2 года назад

@@marksahlgreen9584 make sure you add both 7(1) and 7(8) together it will be 7(9), in the last step it will be 1=7 + 31(-2) +7(8). 4years old but I hope this helps :)