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)

Re Duplication.
At review a few suggested that superscripts be added.  This was done leaving the original intact with the author having a choice to accept either.  Unfortunately this hasn't been done.

As "n" does not appear in the expression, what would be the effect if the first "m" was substituted for "n", or conversely, the second?

As scholars cannot edit this (and it seems neither can Danish) then Danish may ask levik to do the necessary edit.

Posted by brianjn on 2012-12-02 17:21:53