Two positive integers, p and q are connected by p=q+1. By using the binomial expansion, show that the expression p^2n-2nq-1 can be divided exactly by q^2 for all positive integers n. By choosing suitable values for p and n, show that 3^16-33 can be divided exactly by 4, and hence, show that 3^15+5 can be divided exactly by 4.