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How to solve $y^3=x(x+1)$ where $x$ and $y$ are integers ? Can you help me ?

Thanks :)

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  • $\begingroup$ What do you mean “solve”? $\endgroup$ – gen-ℤ ready to perish Jul 15 '19 at 19:48
  • $\begingroup$ With a little effort you should be able to find one or two integer solutions, whose inclusion would improve the Question to asking if one can prove them to be the only solutions. $\endgroup$ – hardmath Jul 15 '19 at 21:34
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Hint: notice that $gcd(x,x+1)=1$ and thus $x=a^3$ and $x+1=b^3$

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Hint

If two numbers $u$, $v$ are coprime and $uv$ is a $r$-th perfect power, then both $u$ and $v$ are $r$-th perfect powers.

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