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On Mordell's equation $y\sp 2-k=x\sp 3$: a problem of Stolarsky
1986
Mathematics of Computation
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On page 1 of his book Algebraic Numbers and Diophantine Approximation, K. B. Stolaxsky posed the problem of solving the equation y2 + 999 = x3 in positive integers. In the present paper we refine some techniques of Ellison and Pethö and show that the complete set of integer solutions of Stolarsky's equation is x = 10, y = ±1, x = 12, y = ±27, x = 40, y = ±251, x = 147, y = ±1782, x = 174, y = ±2295, and x = 22480, y = ±3370501.
doi:10.1090/s0025-5718-1986-0829640-3
fatcat:ynk7yquunbeo5cumdjacrngm7i