Open Access
December 2020 On the exponential Diophantine equation (3m2+1)x+(qm21)y=(rm)z
Nobuhiro Terai, Yoshiki Shinsho
Author Affiliations +
SUT J. Math. 56(2): 147-158 (December 2020). DOI: 10.55937/sut/1611009430


Let m,q,r be positive integers. Then we show that the equation (3m2+1)x+(qm21)y=(rm)z has only the positive integer solution (x,y,z)=(1,1,2) under some conditions. The proof is based on elementary methods and Baker’s method.

Funding Statement

The first author is supported by JSPS KAKENHI Grant (No.18K03247).


Download Citation

Nobuhiro Terai. Yoshiki Shinsho. "On the exponential Diophantine equation (3m2+1)x+(qm21)y=(rm)z." SUT J. Math. 56 (2) 147 - 158, December 2020.


Received: 15 April 2020; Published: December 2020
First available in Project Euclid: 8 June 2022

Digital Object Identifier: 10.55937/sut/1611009430

Primary: 11D61

Keywords: exponential Diophantine equation , Jeśmanowicz’ conjecture , lower bound for linear forms in two logarithms

Rights: Copyright © 2020 Tokyo University of Science

Vol.56 • No. 2 • December 2020
Back to Top