Cornelius, E.F. jun.; Schultz, Phill

Polynomial points

J. Integer Seq. 10(3), Article 07.3.6, 14 p., electronic only (2007)

Summary

Summary: We determine the infinite sequences $ (a_k)$ of integers that can be generated by polynomials with integral coefficients, in the sense that for each finite initial segment of length $ n$ there is an integral polynomial $ f_n(x)$ of degree $ <n$ such that $ a_k=f_n(k)$ for $ k=0,1,\dots, n-1$.

Mathematics Subject Classification

20K21, 20K25, 20K30, 13F20, 15A36

Keywords/Phrases

mixed Abelian groups, Lagrange interpolation polynomials, integral polynomials, integral root basis, baer-specker group, Pascal's matrix

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