Original scientific paper

The extendibility of D(4)-pairs {F_2k, F_2k+6} and {P_2k, P_2k+4}

Ljubica Baćić Đuračković orcid.org/0000-0002-8634-4853 ; Primary School Nikola Andrić, 32000 Vukovar, Croatia
Alan Filipin ; Faculty of Civil Engineering, University of Zagreb, 10 000 Zagreb, Croatia

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.

Keywords

Diophantine tuples; simultaneous Diophantine equations

Hrčak ID:

165783

URI

https://hrcak.srce.hr/165783

Publication date:

15.9.2016.

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