# Thread: Fermat's little theorem help!

1. ## Fermat's little theorem help!

What is the remainder when 132^75 is divided by 37?

I really am confused even though the problem gives a hint that I should use Fermat litle theorem

2. Originally Posted by nhunhu9
What is the remainder when 132^75 is divided by 37?

I really am confused even though the problem gives a hint that I should use Fermat litle theorem
Do you know Fermat's little theorem?

3. Originally Posted by nhunhu9
What is the remainder when 132^75 is divided by 37?

I really am confused even though the problem gives a hint that I should use Fermat litle theorem

$132^{75}=\left(132^{37}\right)^2\cdot 132$ , and now apply FlT .

Tonio

4. Originally Posted by nhunhu9
What is the remainder when 132^75 is divided by 37?

I really am confused even though the problem gives a hint that I should use Fermat litle theorem
Here is the theorem:

$a^{p-1}\equiv 1 \ \mbox{(mod p)}$

5. Originally Posted by dwsmith
Here is the theorem:

$a^{p-1}\equiv 1 \ \mbox{(mod p)}$
If $a\ne zp$.