A new algorithm to search for small nonzero |𝑥³-𝑦²| values

Calvo, I.; Herranz, J.; Sáez, G.

doi:10.1090/S0025-5718-09-02240-6

A new algorithm to search for small nonzero $|x^3-y^2|$ values
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by I. Jiménez Calvo, J. Herranz and G. Sáez PDF

Math. Comp. 78 (2009), 2435-2444 Request permission

Abstract:

In relation to Hall’s conjecture, a new algorithm is presented to search for small nonzero $k=\lvert x^3-y^2\rvert$ values. Seventeen new values of $k<x^{1/2}$ are reported.

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