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

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

2010-05-20

arxiv.org/abs/1005.3624v1

Mathematics

Number Theory

Scientific paper

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.

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