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.