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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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Solution Parametric Solution | Comment 1 of 6

One set of solutions is x=y=4*k^5 and z=2*k^2 for k>=1

Then for any k: (4*k^5)^2 + (4*k^5)^2 = 16*k^10 + 16*k^10 = 32*k^10 = (2*k^2)^5

  Posted by Brian Smith on 2010-05-10 13:34:42
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