Home›Open Questions›Does the Erdos-Straus equation 4/n = 1/x + 1/y + 1/z really have a positive-integer solution for every integer n of 2 or more?Open QuestionsDoes the Erdos-Straus equation 4/n = 1/x + 1/y + 1/z really have a positive-integer solution for every integer n of 2 or more?Citation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Does the Erdos-Straus equation 4/n = 1/x + 1/y + 1/z really have a positive-integer solution for every integer n of 2 or more?." Accessed August 30, 2026. https://mathematics.interactiveatlas.org/open-questions-index/question-erdos-straus-solution-exists-every-n.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Does the Erdos-Straus equation 4/n = 1/x + 1/y + 1/z really have a positive-integer solution for every integer n of 2 or more?. Retrieved August 30, 2026, from https://mathematics.interactiveatlas.org/open-questions-index/question-erdos-straus-solution-exists-every-nCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-does-the-erdos-straus-equation-4-n-1-x-1, author = {Mathematics Atlas}, title = {Does the Erdos-Straus equation 4/n = 1/x + 1/y + 1/z really have a positive-integer solution for every integer n of 2 or more?}, year = {2026}, url = {https://mathematics.interactiveatlas.org/open-questions-index/question-erdos-straus-solution-exists-every-n}, note = {Accessed August 30, 2026} }Copy BibTeXOpen QuestionCross-Tradition ConnectionsSourcesComments (0)Reader Challenges (0 open reader challenges)Open QuestionComputer search has confirmed the equation solvable for every n up to 10^17, and modular identities cover infinitely many residue classes, but no argument closes the remaining, conjecturally empty, set of exceptions for every n at once.What would resolve this A general proof, or a genuine counterexample, covering every integer n rather than a further extension of the verified range.OpenNumber theoryErdos-Straus Conjecture (Wikipedia)Cross-Tradition ConnectionsQuestion OnErdos-Straus Conjecture, Conjectures Well-attested Source Erdos-Straus Conjecture (Wikipedia)tier 2SourcesErdos-Straus Conjecture (Wikipedia)tier 2WikipediaVerification and progress sectionsView the SourceComments (0)No comments yet. Be the first to share a thought.Sign in to join the discussion.Reader Challenges (0 open reader challenges)No disputes yet. Spotted an error or a better source? Open the first one.Sign in to dispute this or suggest a correction.View At A Past YearThe atlas records no dated fact of its own for this entry, so there is no other year to choose.Show This Year