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.)

It seems to me that the two examples that were given are the only suitable cases. You need 2aČ+1=bČ so bČ-1=2aČ -- obviously b must be odd --- if b=2k+1 we get to 2K(K+1)=aČ that is only satisfied for k=0 or k=1.

Posted by e.g. on 2005-07-13 17:18:01