Let A be an integer, P an odd prime and n=3 be the smallest integer for which A^n  1 is divisible by P.
Determine the smallest integer m for which (A+1)^m  1 is divisible by P.
If A=4 and n=3, [A^n  1] = 63 which is divisible by P=3
With the integer A=4 and the odd prime P=3, m can be equal to the small value of 2... [(A+1)^m  1] = 24 which is still divisible by P=3
Therefore, the minimum value is at most 2.

Posted by Dej Mar
on 20070109 00:59:26 