(Quadratic Residues) - Proof of Euler's Criterion for the Legendre Symbol.

Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship. Beyond this, images of white Jesus are not just blasphemous and criminal, white Jesus is from Satan ( the imposter.) Why? Let's look at what Satan does:
1) He is incredibly narcissistic and promotes himself shamelessly.
2) He misleads and confuses.
3) He pushes people away from Jesus Christ God, the Holy Trinity, the one and only messiah. White Jesus does all three of the above and more -- matching the ways of Satan.

Statues of Christ are equally offensive to God the Christ. While money is the biggest idol, Jesus spoke sufficiently against carved images.
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You can also find me on Tik Tok @reuslovesmath and @polarpiny

In this video, I show you how to prove Euler's criterion. We use Fermat's little theorem, Wilson's theorem and break it into two cases, a quadratic residue case and a nonresidue case.

[HeadphoneTarnish]

Tremendously clear explanation (as usual), Polar Pi.

This playlist on quadratic residues/reciprocity has really helped me get a foothold in a class on algebraic number theory, and I appreciate you making them a lot.

How about a series on split-primes and arithmetic progressions :D

[alirezakhodaie]

I am watching your videos as a part of my cryptography course, and I wanted to thank you for your content sir.

[blissfulmountain]

Thank you so much! This is the first time I actually understand this

[gigispace]

this playlist is truly amazing!! (like always) thankssss

[sagarsuryawanshi]

Thank you so much sir, all videos are very Useful

[willnewman]

That is a pretty cool proof. I am used to the more fancy ways of proving things like these, so it is interesting to see how you can prove them without knowing so many other things. I felt the same way about your video on Fermat's Little Theorem.

[НиколайЩекин-цч]

Could you, please, explain how we know that x0 meets the criteria of Fermats Little Theorem, namely gcd(x0, p) = 1

[ivancasgc]

Hi sir, I didn't get where the disequation "1<i<(p-1/2)" comes from. Can you please explain me? Thank you very much.

[mzoon]

what if I want to prove phi(n^2) = n phi (n), any clues Polar Pi?

[sagarsuryawanshi]

Sir in this proof add one more case; if p|a then (a/p)=0
Please consider my comment

[nondrip]

great video, but what the fuck is that description lmao