Question

State the Euler's theorem ​

Answer 1

Answer:

The generalization of Fermat's theorem is known as Euler's theorem. In general, Euler's theorem states that, “if p and q are relatively prime, then ”, where φ is Euler's totient function for integers. That is, is the number of non-negative numbers that are less than q and relatively prime to q.

Answer 2

Intro:

Euler's theorem is a generalization of Fermat's little theorem dealing with powers of integers modulo positive integers. It arises in applications of elementary number theory, including the theoretical underpinning for the RSA cryptosystem.

Theorem :

Let n be a positive integer, and let
a be an integer that is relatively prime to n. Then

aϕ(n)≡1. (mod n )

where
ϕ(n) is Euler's totient function, which counts the number of positive integers
≤n which are relatively prime to n.

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