Do I just need to keep taking out factors of 3747 and computing the smaller numbers mod 4001 until I have reduced it? The largest exponent I can raise 457 to that doesn't produce a number in scientific notation with my calculator is 3 :S
Use the fact that 4001 is a prime to compute , and find an integer k such that .
So I used Fermat's little theorem to reduce the problem initially:
reduces to just:
How can I reduce things further without taking all day?
Thanks.
Do I just need to keep taking out factors of 3747 and computing the smaller numbers mod 4001 until I have reduced it? The largest exponent I can raise 457 to that doesn't produce a number in scientific notation with my calculator is 3 :S