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On multiplicative decompositions of polynomial sequences, I

Volume 184 / 2018

L. Hajdu, A. Sárközy Acta Arithmetica 184 (2018), 139-150 MSC: 11N25, 11N32, 11D09. DOI: 10.4064/aa170620-13-12 Published online: 8 February 2018

Abstract

We consider the multiplicative decomposability of the set of values assumed by a quadratic polynomial. First we show that any large set of shifted squares is multiplicatively primitive. Then we sharpen and extend this result in various directions.

Authors

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

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