- #1

- 70

- 1

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?