Original Articles

The ternary exponential Diophantine equation concerning Pythagorean triplets

Published in: Quaestiones Mathematicae
Volume 38 , issue 4 , 2015 , pages: 483–494

DOI: 10.2989/16073606.2014.981698

Author(s): Han Di School of Mathematics, P.R. China , Zhang Wenpeng School of Mathematics, P.R. China

Keywords: 11D61 , 11D61

Abstract

Let r be a positive integer with r > 1, and let m be a positive even integer. Further let a=|V(m, r)|, b=|U (m, r)| and c=m²+1, where V (m, r) + U (m, r)√−1=(m+^√−1)^r . In this paper, using the Gel^′ fond-Baker method, we prove that if 2 | r and m>max(10¹⁵, 2r3), then the equation ax+b^y=c^z has only the positive integer solution (x, y, z)=(2, 2, r).

« Transversals in 5-uniform hypergraphs and total domination in graphs with minimum degree five

A numerical scheme for solving differential equations with space and time-fractional coordinate derivatives »