Fermat's Little Theorem

Fermat's Little Theorem.  If p is prime and  a is not a multiple of p then    $a^{p-1}\equiv 1\left(\mathrm{mod}p\right)$

Questions.
Based on this theorem what can you say if you are given the following information?

1.        1997  is a prime             Therefore,   ${25}^{1996}\equiv \_?\_\left(\mathrm{mod}1997\right)$

2.         ${13}^{6556}\equiv 1780$ (mod 6557)       Therefore,  __________?_____

3.        $5^{29340}\equiv 1\left(\mathrm{mod}29341\right)$         Therefore,  _______?_______

Calculations, some relating to the questions above.

This follows from the fact that 1997 is  a prime and a direct application of Fermat's Little Theorem

We could predict that 6557 is not prime by the contrapositive of Fermat's Little Theorem

The converse of Fermat's Little Theorem is false.  If $a^{p-1}\equiv 1\left(\mathrm{mod}p\right)$    then we can't conclude that p is prime.  Numbers that illustrate this fact are called psuedoprimes.

$341=11\times 31$ is a psuedoprime to the base 2, but not to the base 7.

$29341=13\times 37\times 61$ is a pseudoprime to a surprising number of bases.  

In fact, 29341 is a pseudoprime to every prime base other than its prime divisors.  Such a number is called a Carmichael number