On the Diophantine Equation 3^x+5^y.19^z=u^2

Xu Ai-juan; Deng Mou-jie

Xu Ai-juan College of Information Science and Technology, Hainan University Haikou 5702288, China
Deng Mou-jie College of Information Science and Technology, Hainan University Haikou 5702288, China

Keywords: Exponential Diophantine equation, elementary methods, non-negative integer solutions.

Abstract

In this paper, we study the Diophantine equation 3^x+5^y.19^z= u². Using elementary methods we show that this Diophantine equation has exactly three solutions (x,y,z,u), namely: (1,0,0,2), (4,0,1,10) and (2,2,1,22).

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