Glasnik Matematicki, Vol. 52, No. 1 (2017), 23-43.

DIOPHANTINE TRIPLES WITH VALUES IN THE SEQUENCES OF FIBONACCI AND LUCAS NUMBERS

Florian Luca and Augustine O. Munagi

The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Private Bag X3, Wits 2050, South Africa
e-mail: florian.luca@wits.ac.za

The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Private Bag X3, Wits 2050, South Africa
e-mail: Augustine.Munagi@wits.ac.za


Abstract.   Let FL={1,2,3,4,5,7,8,11,13,18,21, … } be the set consisting of all Fibonacci and Lucas numbers with positive subscripts. We find all triples (a,b,c) of positive integers a < b < c such that ab+1, ac+1, bc+1 are all members of FL.

2010 Mathematics Subject Classification.   11B39, 11D09, 11D45, 11D75.

Key words and phrases.   Diophantine triples, Fibonacci numbers, Lucas numbers.


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DOI: 10.3336/gm.52.1.03


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