[Jtsummers]

The trick is to do the modulus before the exponentiation. It gives the same result.

  n^4 % x = m
  == (n % x)^4 % x = m

By way of demonstration:

  n = 18, x = 15
  18^4 = 104976 = 6 (mod 15)
  ----
  18 % 15 = 3
  3^4 = 81 = 6 (mod 15)

A very handy result to remember for cases where you don't want to use or don't have easy access to arbitrary precision integers.

[anthk]

Well, this doesn't need much of a demonstration. The rest of a division will be the same "visually" if you keep "stacking" the same number on top.