Rado Numbers for Fibonacci Sequences and a Problem of S. Rabinowitz

Heiko Harborth and Silke Maasberg

A chapter in Applications of Fibonacci Numbers, 1996, pp 143-153 from Springer

Abstract: Abstract In every k-coloring of the first N natural numbers (k ≥ 2), does there exist a monochromatic s-term Fibonacci sequence (s ≥ 3), that is, a sequence f 1 ,f 2 ,…,f 8 where f n + 2 = f n + 1+ f n , n ≥ 1, and f1,f2 are arbitrary natural numbers? In case of existence, the smallest N with this property is called Rado number RaF(k,s) for Fibonacci sequences. For s = 3 the numbers RaF(k, 3) are known as Schur numbers [9]. A similar question for Rado numbers of second order linear recurrences was posed by S. Rabinowitz [12].

Date: 1996
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DOI: 10.1007/978-94-009-0223-7_13

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