Glasnik Matematicki, Vol. 50, No. 1 (2015), 17-24.

TRIBONACCI DIOPHANTINE QUADRUPLES

Carlos Alexis Gómez Ruiz and Florian Luca

Departamento de Matemáticas, Universidad del Valle, 25360 Cali, Calle 13 No 100-00, Colombia
e-mail: carlos.a.gomez@correounivalle.edu.co

School of Mathematics, University of the Witwatersrand, P. O. Box Wits, South Africa
e-mail: florian.luca@wits.ac.za


Abstract.   In this paper, we show that there does not exist a quadruple of positive integers a1 < a2 < a3 < a4 such that aiaj + 1 (i≠ j) are all members of the Tribonacci sequence (Tn)n≥ 0.

2010 Mathematics Subject Classification.   11B37, 11B39, 11D61.

Key words and phrases.   Quadruples Diophantine, Tribonacci numbers.


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DOI: 10.3336/gm.50.1.02


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