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- Integer solutions of $x^3+y^3=z^2$ 12 answers
My question concerns the diophantine equation $a^3 + b^3 = c^2$. I know one solution: $1^3 + 2^3 = 3^2$. But this is special in (at least) two ways: the $a$ and $b$ are not coprime; the solution is a special case of the identity: sum of the first $n$ cubes $=$ the square of the $n$th triangular number.
Are there other solutions?
If not, is there an elementary proof of the fact?