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Periodica Mathematica Hungarica

, Volume 58, Issue 1, pp 59–70 | Cite as

On the family of diophantine triples {k + 1, 4k, 9k + 3}

  • Bo He
  • Alain Togbé
Article

Abstract

We prove that if k is a positive integer and d is a positive integer such that the product of any two distinct elements of the set {k + 1, 4k, 9k + 3, d} increased by 1 is a perfect square, then d = 144k 3 + 192k 2 + 76k + 8.

Key words and phrases

Diophantine m-tuple Pell equation Diophantine approximation linear forms in logarithms 

Mathematics subject classification numbers

11D09 11D45 11B37 11J68 11J86 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of Mathematics Key Laboratory of Numerical Simulation of Sichuan ProvinceNeijiang Normal UniversityNeijiangP. R. China
  2. 2.Department of MathematicsPurdue University North CentralWestvilleUSA

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