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

Eva G. Goedhart; Helen G. Grundman

arxiv: 1304.6413 · v2 · pith:7HZCTUBXnew · submitted 2013-04-23 · 🧮 math.NT

On the Diophantine equation N X² + 2^L 3^M = Y^N

Eva G. Goedhart , Helen G. Grundman This is my paper

classification 🧮 math.NT

keywords diophantineequationlucaresultswangbiludefectivegeneralizing

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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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On the Diophantine equation N X² + 2^L 3^M = Y^N

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