- #1

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For every prime number n, there exist positive integers (k,l,m) such that

k(m

^{2}-n

^{2})=2(m

^{3}+n

^{3}-lm)

some examples (there could be several/many solutions for a given n)

{n,k,l,m}

{2, 14, 8, 2}

{3, 59, 264, 1}

{5, 53, 192, 3}

{7, 71, 264, 5},{7, 239, 6080, 1}

{11, 163, 1856, 5}

If the statement is true for prime n's, it can be shown to hold for composite n's as well.

Thanks, Mathador