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Concerning Difference Sets

Published online by Cambridge University Press:  20 November 2018

T. G. Ostrom
T. G. Ostrom*
Affiliation:
Montana State University
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A set of integers {a0, a1, … , an} is said to be a difference set modulo N if the set of differences {ai — aj (i,j = 0, 1, … , n) contains each non-zero residue mod N exactly once. It follows that N and n are connected by the relation N = n2 + n + 1. If {a0, a1 … an} is a difference set mod N, so is the set {a0 + s, a1 + s, … , an + s} (s = 0, 1, … , N). These difference sets form a finite projective plane of N points, with each difference set constituting a line in the plane.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 421 - 424
Copyright
Copyright © Canadian Mathematical Society 1953

References

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