Fermat's little theorem help!

**nhunhu9** · January 17th 2011, 06:25 PM

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

**dwsmith** · January 17th 2011, 06:31 PM

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?

**tonio** · January 17th 2011, 06:36 PM

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

**dwsmith** · January 17th 2011, 07:11 PM

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:

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

**Drexel28** · January 17th 2011, 08:16 PM

Originally Posted by dwsmith

Here is the theorem:

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

If $a\ne zp$ .

Thread: Fermat's little theorem help!