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

Xu Ai-juan, Deng Mou-jie

Abstract


In this paper, we study the Diophantine equation 3^x+5^y.19^z=u^2. 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).

Keywords


Exponential Diophantine equation; elementary methods; non-negative integer solutions.

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References


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