Question

let \(m\) be any positive integer, prove that if \(p\) is a prime, then
\(m^{a}≡m\) mod \(p\)
for all nonnegative integers
\(a≡1\) mod \(p-1\)
(Consider both when \(p\) divides \(m\) and \(p\) doesn't divide \(m\))

Answer 1

For solving this type of application, you will have to have a detailed concept of Prime and Co-prime