The complete solution of the Diophantine equation (4 m 2 + 1) x + (5 m 2 - 1) y = (3 m) z

Abstract

In this short note we give all solutions to the exponential Diophantine equation (4 m 2 + 1) x + (5 m 2 - 1) y = (3 m) z where 20 < m < 90 and m 3 (m o d 6). In view of earlier theorems of Terai, and of Su and Li, this result yields a complete solution set to a problem of Terai.