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: Solution
by Bob Smith)
Using the three equations. Eliminate b and d to get a quadratic in c. One of the roots for c gives an equation for d that is negative.
Posted by Bractals
on 2005-07-14 03:24:53