On Residue Difference Sets
- 1 January 1953
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 5, 425-432
- https://doi.org/10.4153/cjm-1953-047-3
Abstract
In recent years the subject of difference sets has attracted a considerable amount of attention in connection with problems in finite geometries [4]. Difference sets arising from higher power residues were first discussed by Chowla [1], who proved that biquadratic residues modulo p form a difference set if (p — l )/4 is an odd square. In this paper we shall prove a similar result for octic residues and develop some necessary conditions which will eliminate all odd power residue difference sets and many others. We also prove that a perfect residue difference set (that is, one in which every difference appears exactly once) contains all the powers of 2 modulo p.Keywords
This publication has 3 references indexed in Scilit:
- The quintic character of 2 and 3Duke Mathematical Journal, 1951
- Cyclic projective planesDuke Mathematical Journal, 1947
- Cyclotomy, Higher Congruences, and Waring's ProblemAmerican Journal of Mathematics, 1935