Modular makes everything so easy! Even if you don't know too much of it , it still useful like a congruent to b modulo n can be written as a = kn + b for some integer k and it just becomes a linear equation thereafter. Also syber make this a series ;)
@@SyberMath At 6:39 it doesnt just jave 2 solutions in mod 7 but an infinte mumber because as you said you can add any multiple of 7 so 12 for e.g. is another solution since 12 squared plus 3 equals 147 which is a multiple of 7.
Awesome video! I am preparing for the olympiad so it was fun to see another perspective on modular arithmetic. Great explanation. Greetings from Poland! ❤💕💖
Modular arithmetic is great for finding the last digits of very large exponents... like 7^55, for example. 49 is congruent to -1 (mod 10), 7^4 is congruent to -1^2 = 1 (mod 10) . 55 is basically 13*4 + 3, so the last digit is the last digit of 7^3, which is 3.
This video reminds me of all the theorems and basics that I learned for modulo like fermat,Euler totient function,Wilson theorem,Chinese remainder theorem(for solving 3 congruent modulo).great video,u can make a video on each theorem briefly if u can
I think those would be unlike the videos in this channel, since I think videos are made to help in problem solving, not for teaching itself. There are some MIT OCW lectures on it though, they are great
Broo i like modular so much beacaus we can tested in real life and make life easier !!! ofcorse now we computers but it so intersting when we challenge our brain 😍😍
TEMPS-HASARD MODULO 3 Pour en revenir au sujet qui nous occupe, dans le monde subatomique, il se pourrait que les phénomènes ne suivent pas une ligne de temps unique, ce qui est conforme à la théorie de la gravité quantique et de la « non-existence » temporelle.
couldnt understand the first example (x^2 +3_=0(mod7)after the whole adding 7 to both sides thing. To be specific, you equaled 7 to 0,which has been defined as 7's remainder and which is not the number itself... So how can one just add ita remainder to one side, and the dividend to the other..? A reply would be much appreciated
Adding 7 and 0 are equivalent because 7 is congruent to 0 mod 7. You can also think of it this way: all numbers in the form 7k where k is an integer are congruent mod 7. 7 and 0 are in the same group in that sense. All integers can be grouped into 7 groups mod 7 like 7k 7k+1 7k+2 7k+3 7k+4 7k+5 and 7k+6. Any integer can be represented in one of these forms. I hope this helps.
-3 and 4 are congruent mod 7 because they can both be written as 7k+4. Basically they are in the same group (referring to groups I mentioned in my previous reply)
After repeatedly watching this i am able to understand so basically if u see for eg 28 is a multiple of 7 so remainder is 0 it can be written as 28 congruent to 0 (mod7 )now if you're to add 7 to 28 it becomes 35 since we're not even into the quotient when we write in modular form 35 also is congruent to mod7 you see so the remainder is 0 so if you are to add add 7 to rhs it still should give the same remainder of -3 that's it .
at 8:38 why are we squaring residues of 4 to check if sol exists or not. I did it using even no as : 2k and Odd no as :2k+1 taking modulo of these two I concluded solution doesn't exists but i don't understand how did you do it usig residues of 4
To find out which number squared leaves a remainder of 2 upon division by 4, we need to check the remainders for all possible numbers which are represented by 4 numbers: 0,1,2,3. Any number greater than these fall into one of these categories by the remainder they leave upon division by 4.
2:42 would 2 and 3 be valid answers? I agree that 11 is congruent to 5 mod 6, but mod 2 would be 1, and mod 3 would be 2, properly. I suppose one can say that 11 is congruent to 5 mod 3 in the same way you can say it's -1 mod 3, as basically in mod n we can add or subtract kn where k is an integer. Is that the right direction?
@@SyberMath Yeah exams and all that stuff Finally I am free and can comment as much as I want Thank you once again for keeping me entertained with your math problems during these tough times
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