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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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re: True? Comment 9 of 9 |
(In reply to True? by e.g.)

a=12, b=17

2(12)^2 + 1 = 289 = 17^2   (let k=8)

This is true using c=2, d=3: (12 + 2 + 3 = 17)

So, there are other solutions... haven't found a counterexample or managed a written proof, however.

 

 


  Posted by gail on 2005-07-19 06:08:17
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