## Polynomial points

### 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