Squares and difference sets in finite fields
Langue
en
Article de revue
Ce document a été publié dans
Integers : Electronic Journal of Combinatorial Number Theory. 2013, vol. 13, p. 5 pp
State University of West Georgia, Charles University, and DIMATIA
Résumé en anglais
For infinitely many primes $p=4k+1$ we give a slightly improved upper bound for the maximal cardinality of a set $B\subset \ZZ_p$ such that the difference set $B-B$ contains only quadratic residues. Namely, instead of the ...Lire la suite >
For infinitely many primes $p=4k+1$ we give a slightly improved upper bound for the maximal cardinality of a set $B\subset \ZZ_p$ such that the difference set $B-B$ contains only quadratic residues. Namely, instead of the "trivial" bound $|B|\leq \sqrt{p}$ we prove $|B|\leq \sqrt{p}-1$, under suitable conditions on $p$. The new bound is valid for approximately three quarters of the primes $p=4k+1$.< Réduire
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