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Sophie Squares (Posted on 2005-07-13) Difficulty: 4 of 5
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.)

See The Solution Submitted by Gamer    
Rating: 3.2500 (4 votes)

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Hints/Tips re(2): Solution | Comment 8 of 9 |
(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

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