Consider all possible pairs (M, N) of positive integers that satisfy this equation:

          M2 = N(M+N) - 1

• If this equation has a finite number of solutions, then list all of them.

• If the total number of solutions is infinite, then find the general forms of M and N with valid reasoning.

Note: Extra credit wii be given for a semi-analytic (hand calculator and p&p) solution.