A problem asks to find all possible pairs (x, y) of positive integers that satisfy the equation:(adsbygoogle = window.adsbygoogle || []).push({});

x^{3}= y^{2}– 15

There are 2 pairs (so far) that satisfy the equation:

x = 1, y = 4

x = 109, y = 1138

It's possible that these 2 points are the only two positive integer solutions.

Siegel's theorem states that an elliptic curve can have only a finite number of points with integer coordinates.

Could there be other points for that curve? If not, how to prove that these 2 points are the only solutions?

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# Elliptic curves

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