Some of the things I've learned every day since Oct 10, 2016
96: Euler’s Theorem (Number Theory)
January 20, 2017Posted by on
Euler’s Theorem is a sort of extension of Fermat’s Little Theorem. One way of stating Fermat’s is that where is prime and is any integer,
whereas Euler’s Theorem makes the more general statement that if are simply two coprime integers and is Euler’s totient function,
The reason Fermat’s is a valid special case of Euler’s is because when is prime, .
[The congruence in the statement of Euler’s theorem is actually equivalent (‘if and only if’) to being coprime.]