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On Arithmetic Properties of Products and Shifted Products

In: Analytic Number Theory

Author

Listed:
  • Joël Rivat

    (Université d’Aix-Marseille, Institut de Mathématiques de Marseille, CNRS UMR 7373)

  • András Sárközy

    (Eötvös Loránd University, Department of Algebra and Number Theory)

Abstract

Let 𝒜 $$\mathcal{A}$$ and ℬ $$\mathcal{B}$$ be large subsets of { 1 … , N } $$\{1\ldots,N\}$$ . Arithmetic properties of the products ab, resp. of the shifted products ab + 1 with a ∈ 𝒜 $$a \in \mathcal{A}$$ , b ∈ ℬ $$b \in \mathcal{B}$$ are studied. In particular, it is shown that the sum of digits of the products ab is well distributed, and the size of the subsets 𝒜 , ℬ ∈ { 1 … , N } $$\mathcal{A},\mathcal{B}\in \{ 1\ldots,N\}$$ with the property that ab + 1 is always squarefree is estimated.

Suggested Citation

  • Joël Rivat & András Sárközy, 2015. "On Arithmetic Properties of Products and Shifted Products," Springer Books, in: Carl Pomerance & Michael Th. Rassias (ed.), Analytic Number Theory, pages 345-355, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22240-0_21
    DOI: 10.1007/978-3-319-22240-0_21
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