# Fermat's little theorem help!

• Jan 17th 2011, 06:25 PM
nhunhu9
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 :(
• Jan 17th 2011, 06:31 PM
dwsmith
Quote:

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?
• Jan 17th 2011, 06:36 PM
tonio
Quote:

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 :(

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

Tonio
• Jan 17th 2011, 07:11 PM
dwsmith
Quote:

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:

$\displaystyle a^{p-1}\equiv 1 \ \mbox{(mod p)}$
• Jan 17th 2011, 08:16 PM
Drexel28
Quote:

Originally Posted by dwsmith
Here is the theorem:

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

If $\displaystyle a\ne zp$.