# Number theory question 3-3

• October 18th 2012, 09:05 AM
maximus101
Number theory question 3-3
Show that if $p$ is prime and $m \equiv n(mod p-1)$, then for any integer
$a$:

$a^{m} \equiv a^{n} (mod p)$
• October 26th 2012, 02:55 AM
Salahuddin559
Re: Number theory question 3-3
Use fermat's little theorem. Simply put, if m == n (mod (p - 1)), m - n = k(p - 1), for some integer k. Now, use both sides as powers of a, some number a. a^(k(p - 1)) can be written as (a^(p - 1))^k, where p is a prime.

Salahuddin
Maths online