On the Diophantine equation N X² + 2ˡ 3ᵐ = Yⁿ

Goedhart, Eva G.; Grundman, Helen G.

doi:10.1016/j.jnt.2014.02.008

arXiv 2013-04-23 DOI 10.1016/j.jnt.2014.02.008 0 views

On the Diophantine equation N X² + 2ˡ 3ᵐ = Yⁿ

Goedhart, Eva G. · Grundman, Helen G.

Number Theory 11D41, 11D61

Original · EN

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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