## On multiplicative decompositions of polynomial sequences, III

### Volume 193 / 2020

Acta Arithmetica 193 (2020), 193-216
MSC: 11N25, 11N32, 11D41.
DOI: 10.4064/aa190410-23-7
Published online: 24 January 2020

#### Abstract

In two earlier papers we studied the multiplicative decomposability of polynomial sequences $\{f(x):x\in \mathbb Z ,f(x) \gt 0\}$. Here we extend this problem by considering also sequences which can be obtained from sequences of this type by changing “not too many” elements of them. In particular, we prove the multiplicative analogue of a theorem of Szemerédi and the second author (related to a problem of Erdős).