Rad HAZU, Matematičke znanosti, Vol. 20 (2016), 27-35.

THE EXTENDIBILITY OF D(4)-PAIRS {F_2k, F_2k+6} AND {P_2k, P_2k+4}

Ljubica Baćić Đuračković and Alan Filipin

Faculty of Civil Engineering, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: filipin@master.grad.hr

Abstract.   Let k ≥ 1 be an integer and let F_k be the k-th Fibonacci number and P_k k-th Pell number. In this paper we prove that the pairs {F_2k, F_2k+6} and {P_2k, P_2k+4} cannot be extended to a D(4)-quintuple.

2010 Mathematics Subject Classification.   11D09, 11J68.

Key words and phrases.   Diophantine tuples, simultaneous Diophantine equations.

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