Squares and difference sets in finite fields

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish
Title of host publicationIntegers
Subtitle of host publicationAnnual Volume 2013
PublisherWalter de Gruyter GmbH
Number of pages5
ISBN (Electronic)9783110298161
ISBN (Print)9783110298116
Publication statusPublished - 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