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ALAN M., BİRATLI R. G.
Fundamental journal of mathematics and applications (Online), vol.5, no.3, pp.174-180, 2022 (Peer-Reviewed Journal)
Abstract
Let m" role="presentation" >m be a positive integer. In this paper, we consider the exponential Diophantine equation (6m2+1)x+(3m2−1)y=(3m)z" role="presentation" >(6m2+1)x+(3m2−1)y=(3m)z and we show that it has only unique positive integer solution (x,y,z)=(1,1,2)" role="presentation" >(x,y,z)=(1,1,2) for all m>1." role="presentation" >m>1. The proof depends on some results on Diophantine equations and the famous primitive divisor theorem.