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On multiplicative decompositions of polynomial sequences, III

Volume 193 / 2020

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


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).


  • L. HajduInstitute of Mathematics
    University of Debrecen
    P.O. Box 12
    H-4010 Debrecen, Hungary
  • A. SárközyInstitute of Mathematics
    Eötvös Loránd University
    Pázmány Péter sétány 1/C
    H-1117 Budapest, Hungary

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