Number Theory - & Euler's theorem Fermat's Little Theorem

Congruence

If the integer a and the integer b is divided by a positive integer equal to the number m of the remainder, called a, b congruent modulo m, referred to as a≡b (mod m).

Fermat's Little Theorem

If p is a prime number, then for any integer a, there are A ^p ≡a (MOD p)

For not a multiple of p, a ^{p. 1-} ≡1 (MOD p).

 

 

Euler's theorem

If positive integers a, n prime, then A ^{φ (n)} ≡1 (n-MOD), where φ (n) is the Euler function.

 

 The algorithm better understand some of the competition guidelines.

Simplified multiplication remainder based on the closed mold m.

Extended Euclid

For any integer a, b, there is a pair of integers x, y, satisfying ax + by = gcd (a, b).

Proof blog:

https://blog.csdn.net/synapse7/article/details/19610361