On the Diophantine equation NX2+2L3M = YN

JOURNAL OF NUMBER THEORY

卷:141

Article

Goedhart, Eva G.¹  Grundman, Helen G.¹ 

[1] Bryn Mawr Coll, Dept Math, Bryn Mawr, PA 19010 USA

关键词: Exponential Diophantine equations;    Lehmer sequences;   

DOI  :  10.1016/j.jnt.2014.02.008

来源: Elsevier

【 摘 要 】

We prove that the Diophantine equation NX2 + 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free