Fermat's Little Theorem states "If p is prime and a is an integer, then a^p = a (mod p)"   

Consider this Mersenne prime (that is, prime of the form 2^n-1), which is more than 600 digits long.

Let a be a random integer between 2 and p-1.

Verify the correctness of Fermat's Little Theorem.

This example demonstrates the improvement of Maple 9 with arbitrary-precision integer arithmetic with GMP. Maple 9 computes this summation 25 times faster than Maple 8 (tested on a Pentium 4 1.5 GHz)

You can verify that the above sum is computed correctly by using the knowledge that it asymptotically approaches Pi^2/6.