Euler’s conjecture

In 1769, Leonhard Euler conjectured that for 1<k<n there is no set of positive integers a1,,ak such that


where m is an integer. Lander and Parkin in 1966 disproved the conjecture with this k=4,n=5 counterexample: 275+845+1105+1335=1445. More counterexamples have been discovered since then.

Title Euler’s conjecture
Canonical name EulersConjecture
Date of creation 2013-03-22 16:25:43
Last modified on 2013-03-22 16:25:43
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 7
Author PrimeFan (13766)
Entry type Conjecture
Classification msc 11B13
Classification msc 11D41
Synonym Euler conjectureMathworldPlanetmath