Solutions to $y^2 = x^3 + k$?

prime-numbers number-theory algebraic-number-theory diophantine-equations mordell-curves

Solution 1:

This is a famous class of elliptic curves, called Mordell's equation, or sometimes Mordell-Bachet equation. See also here, or here for some discussions on MSE. For a specific example with $k=2000000$ see also here. A further reference is this article by Keith Conrad.

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