Fermat's little theorem

Printable View

• Nov 19th 2007, 07:07 PM
epsilon
Fermat's little theorem
Hello, I have a test tomorrow and this may or may not be on that test.
Anyway, I can't for the life of me understand what is being asked here:

Use Fermat's little theorem to compute:
3^302 mod 5, 3^302 mod 7, 3^302 mod 11

I've tried to look this up online, but I can't find anything. I just don't understand the connection to Fermat's little theorem, which is :
for p prime and a a pos. integer:
a^(p-1) CONGRUENT 1 (mod p)

Any help would be very appreciated!!
Thanks so much!
• Nov 19th 2007, 07:10 PM
ThePerfectHacker
Quote:

Originally Posted by epsilon
Hello, I have a test tomorrow and this may or may not be on that test.
Anyway, I can't for the life of me understand what is being asked here:

Use Fermat's little theorem to compute:
3^302 mod 5, 3^302 mod 7, 3^302 mod 11

I've tried to look this up online, but I can't find anything. I just don't understand the connection to Fermat's little theorem, which is :
for p prime and a a pos. integer:
a^(p-1) CONGRUENT 1 (mod p)

Any help would be very appreciated!!
Thanks so much!

3^4 = 1 (mod 5) by Fermat theorems.
So (raise to the 75) both sides,
3^300 = 1 (mod 5)
Multiply 3^2 both sides,
3^302 = 3^2 = 9 = 4 (mod 5)

The same thing with the others.
• Nov 19th 2007, 07:24 PM
epsilon
Thanks!
Thank you very much! You've put my mind to ease about the test tomorrow.
• Nov 19th 2007, 09:23 PM
dpe82
Quote:

Originally Posted by epsilon
Thank you very much! You've put my mind to ease about the test tomorrow.

You don't happen to be a Math 240 student at UW-Madison, do you? :p