How many positive integers 'n' are there such that [(2)^n + 1] is divisible by 7 ?

2^n is congruent only to 2, 4, or 1 mod 7, so 2^n+1 is congruent only to 3, 5, or 2 mod 7. Hence there are 0 positive integers n such that 2^n + 1 (or 2^(n+1) for that matter) is divisible by 7.

Posted by Richard on 2004-01-02 10:51:26