### Abstract

Let A and B be large subsets of {1 …, N}. Arithmetic properties of the products ab+1, resp. of the shifted products ab C 1 with a ε A, b ε 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 ε {1 …, N} with the property that ab + 1 is always squarefree is estimated.

Original language | English |
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Title of host publication | Analytic Number Theory |

Subtitle of host publication | In Honor of Helmut Maier's 60th Birthday |

Publisher | Springer International Publishing |

Pages | 345-355 |

Number of pages | 11 |

ISBN (Electronic) | 9783319222400 |

ISBN (Print) | 9783319222394 |

DOIs | |

Publication status | Published - Jan 1 2015 |

### Keywords

- Digit properties
- Large sieve
- Multiplicative characters
- Product of sequences
- Shifted products
- Squares

### ASJC Scopus subject areas

- Mathematics(all)
- Computer Science(all)

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## Cite this

Rivat, J., & Sárközy, A. (2015). On arithmetic properties of products and shifted products. In

*Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday*(pp. 345-355). Springer International Publishing. https://doi.org/10.1007/978-3-319-22240-0_21