### Abstract

For infinitely many primes p = 4k + 1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Z_{p} such that the difference set B - B contains only quadratic residues. Namely, instead of the “trivial” bound (Formula Presented) we prove (Formula Presented), under suitable conditions on p. The new bound is valid for approximately three quarters of the primes p = 4k + 1.

Original language | English |
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Title of host publication | Integers |

Subtitle of host publication | Annual Volume 2013 |

Publisher | Walter de Gruyter GmbH |

Pages | 1037-1041 |

Number of pages | 5 |

ISBN (Electronic) | 9783110298161 |

ISBN (Print) | 9783110298116 |

DOIs | |

Publication status | Published - Jan 1 2014 |

### ASJC Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Squares and difference sets in finite fields'. Together they form a unique fingerprint.

## Cite this

Bachoc, C., Matolcsi, M., & Ruzsa, I. Z. (2014). Squares and difference sets in finite fields. In

*Integers: Annual Volume 2013*(pp. 1037-1041). Walter de Gruyter GmbH. https://doi.org/10.1515/9783110298161.1037