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 True? by e.g.)

I haven't checked to see where you went wrong, but I have the following suitable examples so far:

A      B     C    D
0      1      0     1
2      3      0     1
12   17      2     3
70   99     12    17
408  577   70    99
?      ?       408  577

Posted by Steve Herman on 2005-07-13 17:29:07