Let p and q be two different prime numbers greater than 3.Prove that if their difference is 2^n, then for any two integers n and m,the number S=p^(3m+1)+q^(2m+1) is divisible by 3.

Let p and q be two different prime numbers greater than 3.
Prove that if their difference is 2ⁿ, then for any two integers n and m,
the number S = p^(3m+1) + q^(2m+1) is divisible by 3.

(In reply to Confusing problem by Math Man)

Mathman,

In fairness to Danish, n does appear, as the power of 2.

Otherwise, I agree that there appear to be counter-examples, as the puzzle now stands.

Posted by broll on 2012-12-02 23:41:23