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Many triplets (Posted on 2010-05-10) Difficulty: 2 of 5
Prove that the equation x^2+y^2=z^5 has an infinite number of positive integer solutions.

No Solution Yet Submitted by Ady TZIDON    
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another solution set | Comment 2 of 6 |
(In reply to Parametric Solution by Brian Smith)

For integer k>=0, let x=y=2^(5k+2), z=2^(2k+1).

edit -- this appears to be identical to the first solution.

 

Edited on May 10, 2010, 2:31 pm
  Posted by xdog on 2010-05-10 14:15:00

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