perplexus.info :: Just Math : Many triplets

Many triplets (Posted on 2010-05-10)

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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Parametric Solution

| Comment 1 of 7

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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