On the Diophantine equation N X2 + 2L 3M = YN
Abstract
We prove that the Diophantine equation N X2 + 2L 3M = YN has no solutions (N,X,Y,L,M) in positive integers with N > 1 and gcd(NX,Y) = 1, generalizing results of Luca, Wang and Wang, and Luca and Soydan. Our proofs use results of Bilu, Hanrot, and Voutier on defective Lehmer pairs.
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