A note on the exponential Diophantine equation $(4m²+1)^x + (5m²-1)^y = (3m)^z$

• Autorzy: Jianping Wang , Tingting Wang , Wenpeng Zhang
• Języki publikacji: EN

Abstrakty

EN

Let m be a positive integer. Using an upper bound for the solutions of generalized Ramanujan-Nagell equations given by Y. Bugeaud and T. N. Shorey, we prove that if 3 ∤ m, then the equation $(4m²+1)^x + (5m²-1)^y = (3m)^z$ has only the positive integer solution (x,y,z) = (1,1,2).

Kategorie tematyczne

• 11D61: Exponential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 139
• Numer: 1
• Strony: 121-126

Daty

wydano

2015

Twórcy

autor

Jianping Wang

• College of Science, Chang'an University, Xi'an, Shaanxi, P.R. China

autor

Tingting Wang

• Department of Mathematics, Northwest University, Xi'an, Shaanxi, P.R. China

autor

Wenpeng Zhang

• Department of Mathematics, Northwest University, Xi'an, Shaanxi, P.R. China

Identyfikatory

DOI

10.4064/cm139-1-7