Sets with integral distances in finite fields

Alex Iosevich*, Igor E. Shparlinski, Maosheng Xiong

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
28 Downloads (Pure)


Given a positive integer n, a finite field Fq of q elements (q odd), and a non-degenerate quadratic form Q on Fqn, in this paper we study the largest possible cardinality of subsets ε⊆ Fqn with pairwise integral Q-dis- tances; that is, for any two vectors × = (xi,⋯,xn),y = (yi,.,yn) ∞εA,one has Q(x - y) = u2 for some u ∞ F q.

Original languageEnglish
Pages (from-to)2189-2204
Number of pages16
JournalTransactions of the American Mathematical Society
Issue number4
Publication statusPublished - Apr 2010

Bibliographical note

Copyright 2009 American Mathematical Society. First published in Transactions of the American Mathematical Society, 362(4), 2189-2204, published by the American Mathematical Society. The original article can be found at


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