Abstract and Applied Analysis

The Exponential Diophantine Equation 4 m 2 + 1 x + 5 m 2 - 1 y = ( 3 m ) z

Juanli Su and Xiaoxue Li

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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  +  5 m 2 - 1 y = ( 3 m ) 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

Permanent link to this document
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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