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arXiv · 1406.6307

The Erd\H{o}s-Straus conjecture New modular equations and checking up to $N=10^{17}$

Serge E. Salez
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Abstract

In 1999 Allan Swett checked (in 150 hours) the Erd\H{o}s-Straus conjecture up to $N=10^{14}$ with a sieve based on a single modular equation. After having proved the existence of a "complete" set of seven modular equations (including three new ones), this paper offers an optimized sieve based on these equations. A program written in C++ (and given elsewhere) allows then to make a checking whose running time, on a typical computer, range from few minutes for $N=10^{14}$ to about 16 hours for $N=10^{17}$.

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Serge E. Salez. 2014-06-24. The Erd\H{o}s-Straus conjecture New modular equations and checking up to $N=10^{17}$. https://arxiv.org/abs/1406.6307

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