On the Diophantine equation N X^2 + 2^L 3^M = Y^N

Eva G. Goedhart; Helen G. Grundman

doi:10.1016/j.jnt.2014.02.008

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arXiv · 1304.6413

On the Diophantine equation N X^2 + 2^L 3^M = Y^N

Eva G. Goedhart·Helen G. Grundman

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Abstract

We prove that the Diophantine equation N X^2 + 2^L 3^M = Y^N 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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Eva G. Goedhart, Helen G. Grundman. 2014-04-17. On the Diophantine equation N X^2 + 2^L 3^M = Y^N. https://doi.org/10.1016/j.jnt.2014.02.008

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