Product + Square = Difference of Squares (Posted on 2011-07-03)

Three positive integers P, Q and R, with P < Q < R, are in arithmetic sequence satisfying :
N*P*Q*R + Q^{2} = R^{2} - P^{2}, where N is a positive integer.

Determine all possible quadruplet(s) (P, Q, R, N) that satisfy the above equation, and prove that no other quadruplet satisfies the given conditions.