Basics of Modular Arithmetic
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- Опубликовано: 10 июл 2024
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#NumberTheoryTopics #ModularArithmetic
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ADDITIONAL TOPICS:
Chinese Remainder Theorem
Fermat’s Little Theorem
Euler’s Theorem
Primitive Roots and Power Residues
Hensel’s Lemma
Quadratic Residues and Quadratic Reciprocity
RESOURCES:
en.wikipedia.org/wiki/Modular...
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www.geeksforgeeks.org/modular...
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OMG just on time! I have been taking this lesson for a month and I can't wrap my head around it. Can't wait to finally understand it!
Wonderful!
Yes! finally! I was searching for these!
I love this guy,always consistent,good explanation and good videos. Almost getting to 10k subscribers and he deserves it. Will get there someday bro.😍
I appreciate that! 💖
Really like this topic! I hope you will continue the Modular Arithmetics series
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 ;)
Very neat and elegant introduction to the topic!
Awesome video! I am preparing for the olympiad so it was fun to see another perspective on modular arithmetic. Great explanation. Greetings from Poland! ❤💕💖
Glad it was helpful! 💖
great video man ! keep up the work !
you are a great teacher bro, thanks for taking us through the basics of a topic that is so confusing to many students, great job, excellent tutorial
I appreciate that! 💖
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
One of my favorite topics. And its symbols... feast for my eyes!
Wow, I really do like this video! Hopefully there are many more topics that can be explained like this. Have a nice day
Thank you! You too!
Great, bring more.
Modular arithmetic; one of the most important aspects of mathematics
IT COMES IN ABSTRACT ALGEBRA WHICH COMES IN PHYSICS, CHEMISTRY AND SO ON
That's right!
@@SyberMath ARE YOU REPLYING TO ME?
@@aashsyed1277 hey watch your caps
@@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.
@Sybermath please continue this series.... this is really helpful 😊🤩
YES
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.
Absolutely!
😂 the title should be, Modular Arithmetic: The cheat code to Mathematics!
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*SYBERMATH LOVERS ...*
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Thank you! 💖
@@SyberMath i thought you were bringing quadratic congruence as well :|
@@SyberMath yes!
@@SyberMath i love you!
Syber Math fan here from the Philippines
Can you do video like this a basic olympiad theorem and how to use it, but also longer and deep?, it would help me a lot!
Will try in the future
Good introduction to modulo.
Glad you think so!
Are you coming up with a course on number theory or is it just a randomly posted topic🤔.
After the mod equation video, there's been some requests. No plan on making a course
Sir, how do you make your videos, what software do you use to write on?
Microphone: Blue Yeti USB Microphone
Device: iPad and apple pencil
Apps and Web Tools: Notability, Google Docs, Canva, Desmos
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Love you bro thanks
Np. Thank you! 🥰
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.
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 😍😍
Yes, true
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?
Yes. 11≡1 (mod 2) and 5≡1 (mod 2) so they are congruent
Similarly, 11≡2 (mod 3) and 5≡2 (mod 3) so they are congruent
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)
@SyberMath can k be 0
@@SyberMathcan k be 0
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 .
First, sooo close to 10k subscribers!
Great video
few hours left!
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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.
oh so we are taking mod first of num and then squaring the remainder and again taking mod ? @@SyberMath
another small thing is wilson's theorem
Hey SyberMath , how you doing ?
Pretty good! How are you? Long time no see! 😁
@@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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Haha, thanks!
@@SyberMath WELCOME!