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Hint 2: Use the Chinese Remainder Theorem. You will find it isn't as bad as it usually is.

what is mod? what class do we learn about this?

It's also called "Clock arithmetic" sometimes http://en.wikipedia.org/wiki/Modular_arithmetic

ahhh ok we used this in computer science

so 8mod(3) = 2?

Right.

hmm

thats the fun of it:) I got to eat but will be back in a bit to try more

\[89^{307}\pmod{23}=15\]\[89^{307}\pmod{31} = 15\]15?

Thank you for helping me through.

How much were you able to do by hand?

I used calculator for 13*12*20 (mod 23) and for verifying my answers.

oh hmm can you show me? or maybe a hint?

I like it, it's much better and simpler than mine. Thank you.

I love it when I can use it. It was a little trick I learned in my cryptography class.