### 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: 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

**Squares and difference sets in finite fields.** / Bachoc, C.; Matolcsi, M.; Ruzsa, I.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Squares and difference sets in finite fields

AU - Bachoc, C.

AU - Matolcsi, M.

AU - Ruzsa, I.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - For infinitely many primes p = 4k + 1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Zp 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.

AB - For infinitely many primes p = 4k + 1 we give a slightly improved upper bound for the maximal cardinality of a set B ⊂ Zp 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.

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U2 - 10.1515/9783110298161.1037

DO - 10.1515/9783110298161.1037

M3 - Chapter

SN - 9783110298116

SP - 1037

EP - 1041

BT - Integers: Annual Volume 2013

PB - Walter de Gruyter GmbH

ER -