I recently needed to solve a problem of the form below. Problem: Let K, 0 <= K < 100, be an integer constant. Find solutions (x,N) in (Z+)^2 satisfying the equation: (*) K*x + 1 = N^2 . I don't care what N is, just that K*x + 1 is a perfect square. (Not knowing a good way to solve this exactly, I instead used a computer to spit out the cases with 0 <= g <= 10^6, which was more than enough for now. There are about 1200 solutions for the K that I used.) It would be nice to have one or more parametrized families that give (preferably all) solutions (x,N) to (*). Thanks, Dan P.S. I thought I already posted a similar post Thursday morning, but apparently not. ________________________________________________________________________________________ It goes without saying that .