Complete solution of the Diophantine equation $x^y+y^x=z^z$

Autor:	Cipu, Mihai
Jazyk:	angličtina
Předmět:	matematika mathematics články journal articles exponential Diophantine equation sieving modular computations
Druh dokumentu:	Non-fiction
ISSN:	0011-4642
Abstrakt:	Abstract: The triples $(x,y,z)=(1,z^z-1,z)$, $(x,y,z)=(z^z-1,1,z)$, where $z\in\Bbb N$, satisfy the equation $x^y+y^x=z^z$. In this paper it is shown that the same equation has no integer solution with $\min\{x,y,z\} > 1$, thus a conjecture put forward by Z. Zhang, J. Luo, P. Z. Yuan (2013) is confirmed.
Databáze:	Katalog Knihovny AV ČR
Externí odkaz:	Plný text Full text from SpringerLink