Prove that for all nonnegative integers a and b, such that 2a² + 1 = b², there are two nonnegative integers c and d such that 2c² + 1 = d² and a + c + d = b, or give a counterexample.

(For example if a = 0 and b = 1, or a = 2 and b = 3 then c=0 and d = 1.)

(In reply to Solution by Bractals)

Great job...it was pretty much the approach I was trying, but I couldn't come up with the right substitutions.  How did you come up with c=3a-2b and d=3b-4a?

Thanks

Posted by Bob Smith on 2005-07-13 20:05:16