Abstract
An integer-valued polynomial on a subset S of ℤ is a polynomial f (x) ∊ ℚ [x] with the property f (S) ⊆ ℤ. This article describes the ring of such polynomials in the special case that S is the Fibonacci numbers. An algorithm is described for finding a regular basis, i.e., an ordered sequence of polynomials, the nth one of degree n, with which any such polynomial can be expressed as a unique integer linear combination.
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