On some ternary pure exponential diophantine equations with three consecutive positive integers bases View Full Text


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Article Info

DATE

2019-04

AUTHORS

Ruiqin Fu, Bo He, Hai Yang, Huilin Zhu

ABSTRACT

By using the lower bound of linear forms in two logarithms of Laurent (Acta Arith. 133(4) (2008) 325–348), we give here a new solution that the ternary pure exponential diophantine equation (n+1)x+(n+2)y=nz has no positive integer solutions except for (n,x,y,z)=(3,1,1,2). This proof is very different from Le (J. Yulin Teachers College28(3) (2007) 1–2), in which he used the classification method of solutions of exponential decomposition form equation. Furthermore, we solved completely another similar ternary pure exponential diophantine equation nx+(n+2)y=(n+1)z by using m-adic estimation of linear forms due to Bugeaud (Compos. Math. 132(2) (2002) 137–158). More... »

PAGES

26

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s12044-019-0468-x

DOI

http://dx.doi.org/10.1007/s12044-019-0468-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1112685371


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