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Apr 18, 2012 at 14:21 vote accept Hej
Apr 18, 2012 at 2:18 history edited Noam D. Elkies
Added diophantine-equations and k3-surfaces tags
Apr 18, 2012 at 2:18 comment added Noam D. Elkies You're welcome. The initial solution is found by exhaustive search (scaling from $(16,45,64)$, though this turns out not to be minimal). For further solutions and details, see the answer I just posted [which also explains why I'm editing to include the "k3-surfaces" tag].
Apr 18, 2012 at 2:16 answer added Noam D. Elkies timeline score: 18
Apr 17, 2012 at 19:19 comment added Hej Thanks Noam. How do you find them?
Apr 17, 2012 at 18:11 comment added Noam D. Elkies Yes. $(x,y,z) = (80,225,320)$ works, giving $25^2$, $340^2$, $2400^2$. There are infinitely many other (non-proportional) examples.
Apr 17, 2012 at 17:56 history asked Hej CC BY-SA 3.0