finding the least residue

[snejes]

Using Fermat’s little theorem, find the least residue of 5^38 modulo 13.

I know that the theorem states to use a^p-1 is congruant to 1 (mod p)
but how do i apply this using the above 5^38 mod 13?
any help would be great
snejs

 

[Ishuda]

Using Fermat’s little theorem, find the least residue of 5^38 modulo 13.

I know that the theorem states to use a^p-1 is congruant to 1 (mod p)
but how do i apply this using the above 5^38 mod 13?
any help would be great
snejs

Actually Fermat's little theorem is, if p is a prime
a^p = a mod(p)
We can write that as
a^p-1 = 1 mod(p)
only if a and p are relatively prime. In any case
5²⁸ = 5¹² 5¹² 5² 5²