Abstract

Let $a,\ m$ be positive integers such that $am\not\equiv0\pmod{3}, 2\nmid a$, and $a>3$. We prove that the exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$ has only the positive integer solution $(x,y,z)=(1,1,2)$.

DOI

10.3906/mat-1905-20

Keywords

Diophantine equation, positive integer solution, Fibonacci number

First Page

2561

Last Page

2567

Recommended Citation

DENG, N, WU, D, & YUAN, P (2019). The exponential Diophantine equation $(3am^2-1)^x+(a(a-3)m^2+1)^y=(am)^z$. Turkish Journal of Mathematics 43 (5): 2561-2567. https://doi.org/10.3906/mat-1905-20

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