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 re: True? by Steve Herman)

And one beyond that

A=2378

B=3363

C=408

D=577

There's a definite pattern...A & B of one solution becomes C & D for the next.  I don't think though if you prove that pattern, you've proved it for all A & B.

Bob

Posted by Bob Smith on 2005-07-13 17:43:19