# large exponents with fermats little theorem

• February 24th 2010, 02:04 PM
jias
large exponents with fermats little theorem
I am trying to solve this problem:

use Fermat's little theorem to compute 3^302 mod 5.

I know that with the little theorem you can determine that

3^4 is congruent to 1 mod 5.

After that im not really sure how to apply it.

If anyone could help me with it would be great. thanks.
• February 24th 2010, 08:53 PM
tonio
Quote:

Originally Posted by jias
I am trying to solve this problem:

use Fermat's little theorem to compute 3^302 mod 5.

I know that with the little theorem you can determine that

3^4 is congruent to 1 mod 5.

After that im not really sure how to apply it.

If anyone could help me with it would be great. thanks.

The following operations are done modulo 5:

$3^{302}=\left(3^4\right)^{75}\cdot 3^2=1\cdot 3^2 =$ ...

Tonio