Fermat–Catalan conjecture
generalization of Fermat's Last Theorem and Catalan's conjecture: a^m+b^n=c^k has only finitely many positive-integer solutions where a, b, c are coprime and m, n, k satisfy 1/m+1/n+1/k<1
Facts
4 properties- Instance of
- conjecture
- Defining formula
- \left\{(a,b,c,m,n,k)\in(\mathbb Z^+)^6|1/m+1/n+1/k<1=\gcd\{a,b,c\}\right\}<\infty
- Maintained by WikiProject
- WikiProject Mathematics[3]
- Named after
- Pierre de Fermat[2]
🏷️ Also known as
en Fermat–Catalan conjecture
ar تخمين فيرما كاتالان
cs Fermat-Catalanova domněnka
cs Fermatova-Catalanova domněnka
de Fermat-Catalan-Vermutung
el Εικασία Φερμά-Καταλάν
es Conjetura de Fermat-Catalan
es Conjetura de Fermat–Catalan
fr conjecture de Fermat–Catalan
hu Fermat–Catalan-sejtés
ja フェルマー＝カタラン予想
nl Vermoeden van Fermat-Catalan
pt Conjectura de Fermat-Catalan
ru Гипотеза Ферма-Каталана
sv Fermat–Catalans förmodan
uk Гіпотеза Ферма — Каталана
zh Fermat–Catalan猜想
🔖 Identifiers · 3
- Freebase ID
- /m/05zkdhh
- MathWorld ID
- Fermat-CatalanConjecture
- Microsoft Academic ID (discontinued)
- 2778195789
🔗 Connections
Created notable works 1
Instance of 1
Maintained by WikiProject 1
Named after 1
Press Enter · cited answer in seconds
0 sources
Summary
Fermat–Catalan conjecture is a conjecture[1].