On the diophantine equation $x^y - y^x = c^z$

• Autorzy: Zhongfeng Zhang , Jiagui Luo , Pingzhi Yuan
• Języki publikacji: EN

Abstrakty

EN

Applying results on linear forms in p-adic logarithms, we prove that if (x,y,z) is a positive integer solution to the equation $x^y - y^x = c^z$ with gcd(x,y) = 1 then (x,y,z) = (2,1,k), (3,2,k), k ≥ 1 if c = 1, and either $(x,y,z) = (c^k+1,1,k)$, k ≥ 1 or $2 ≤ x < y ≤ max{1.5×10^{10},c}$ if c ≥ 2.

Kategorie tematyczne

• 11D61: Exponential equations
• 11D41: Higher degree equations; Fermat's equation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 128
• Numer: 2
• Strony: 277-285

Daty

wydano

2012

Twórcy

autor

Zhongfeng Zhang

• School of Mathematics and Information Science, Zhaoqing University, 526061 Zhaoqing, P.R. China

autor

Jiagui Luo

• School of Mathematics and Information Science, Zhaoqing University, 526061 Zhaoqing, P.R. China

autor

Pingzhi Yuan

• Department of Mathematics, South China Normal University, 510631 Guangzhou, P.R. China

Identyfikatory

DOI

10.4064/cm128-2-13