## Abstract and Applied Analysis

### The Exponential Diophantine Equation ${(4{m}^{2}+1)}^{x}+{({5m}^{2}-1)}^{y}={(3m)}^{z}$

#### Abstract

Let m be a positive integer. In this paper, using some properties of exponential diophantine equations and some results on the existence of primitive divisors of Lucas numbers, we prove that if $m>90$ and $3|m$, then the equation ${(4{m}^{2}+1)}^{x} + {({5m}^{2}-1)}^{y}={(3m)}^{z}$ has only the positive integer solution $(x,y,z)=(1,1,2)$.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 670175, 5 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412273314

Digital Object Identifier
doi:10.1155/2014/670175

Mathematical Reviews number (MathSciNet)
MR3198228

#### Citation

Su, Juanli; Li, Xiaoxue. The Exponential Diophantine Equation ${(4{m}^{2}+1)}^{x}+{({5m}^{2}-1)}^{y}={(3m)}^{z}$. Abstr. Appl. Anal. 2014 (2014), Article ID 670175, 5 pages. doi:10.1155/2014/670175. https://projecteuclid.org/euclid.aaa/1412273314

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