Home›Open Questions›Whenever A to the x plus B to the y equals C to the z, with x, y and z all greater than two, do A, B and C really always share a common prime factor?Open QuestionsWhenever A to the x plus B to the y equals C to the z, with x, y and z all greater than two, do A, B and C really always share a common prime factor?Citation FormatsGeneral ReferenceGeneral Reference Citation TextMathematics Atlas. "Whenever A to the x plus B to the y equals C to the z, with x, y and z all greater than two, do A, B and C really always share a common prime factor?." Accessed August 30, 2026. https://dev-mathematics.interactiveatlas.org/open-questions-index/beal-conjecture-open-question.Copy General ReferenceAPA StyleAPA Style Citation TextMathematics Atlas. (n.d.). Whenever A to the x plus B to the y equals C to the z, with x, y and z all greater than two, do A, B and C really always share a common prime factor?. Retrieved August 30, 2026, from https://dev-mathematics.interactiveatlas.org/open-questions-index/beal-conjecture-open-questionCopy APA StyleBibTeXBibTeX Citation Text@misc{mathematicsatlas-whenever-a-to-the-x-plus-b-to-the-y-equa, author = {Mathematics Atlas}, title = {Whenever A to the x plus B to the y equals C to the z, with x, y and z all greater than two, do A, B and C really always share a common prime factor?}, year = {2026}, url = {https://dev-mathematics.interactiveatlas.org/open-questions-index/beal-conjecture-open-question}, note = {Accessed August 30, 2026} }Copy BibTeXOpen QuestionCross-Tradition ConnectionsSourcesComments (0)Reader Challenges (0 open reader challenges)Open QuestionNo complete proof or counterexample has been found since Andrew Beal proposed the conjecture in 1993. Partial results confirm it for many specific combinations of exponents, but a general argument covering every combination, or a single counterexample disproving it, has eluded both professional and amateur attempts despite the million dollar prize Beal has offered.What would resolve this A general proof covering every valid combination of A, B, C, x, y and z, or a single confirmed counterexample: one solution where A, B and C share no common prime factor.OpenNumber theoryBeal Conjecture (Wikipedia)Cross-Tradition ConnectionsQuestion OnBeal Conjecture, Conjectures Well-attested Source Beal Conjecture (Wikipedia)tier 2SourcesBeal Conjecture (Wikipedia)tier 2Wikimedia FoundationStatement sectionView 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