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Mathematics of Computation

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Twenty-fourth power residue difference sets

Author: Ronald J. Evans
Journal: Math. Comp. 40 (1983), 677-683
MSC: Primary 12C20; Secondary 05B10, 10G05, 10L05
MathSciNet review: 689481
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Abstract: It is proved that if p is a $ {\text{prime}} \equiv 1\;\pmod 24$ such that either 2 is a cubic residue or 3 is a quartic residue $ \pmod p$, then the twenty-fourth powers $ \pmod p$ do not form a difference set or a modified difference set.

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Keywords: Power residue difference sets, cyclotomic numbers, Gauss and Jacobi sums
Article copyright: © Copyright 1983 American Mathematical Society