The Erdős-Straus conjecture New modular equations and checking up to N=10¹⁷

2014/06/24 by Salez, Serge E. · 1 citation
#11D68 (Primary) 11N35 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1406.6307

Abstract

In 1999 Allan Swett checked (in 150 hours) the Erdős-Straus conjecture up to N=10¹⁴ 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=10¹⁴ to about 16 hours for N=10¹⁷.

Cited by

• Almost a Complete Proof of the Generalized Erdős-Straus Conjecture: 5/a = 1/b + 1/c + 1/d

Related

• Further verification and empirical evidence for the Erdős-Straus conjecture
• Well-defined Erdös-Straus equations and L.C.M
• Partial Resolution of the Erdös-Straus, Sierpinski, and Generalized Erdös-Straus Conjectures Using New Analytical Formulas
• Solutions to Diophantine Equation of Erdos-Straus Conjecture
• Almost a Complete Proof of the Generalized Erdős-Straus Conjecture: 5/a = 1/b + 1/c + 1/d