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arXiv:1005.3624 [math.NT]AbstractReferencesReviewsResources

On Arithmetic Progressions in Recurrences - A new characterization of the Fibonacci sequence

Akos Pinter, Volker Ziegler

Published 2010-05-20Version 1

We show that essentially the Fibonacci sequence is the unique binary recurrence which contains infinitely many three-term arithmetic progressions. A criterion for general linear recurrences having infinitely many three-term arithmetic progressions is also given.

Categories: math.NT
Subjects: 11B25, 11B39, 11J87
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