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Differences of residues (mod p)

✍ Scribed by E.G Straus

Book ID: 103218581
Publisher: Elsevier Science
Year: 1976
Tongue: English
Weight: 145 KB
Volume: 8
Category: Article
ISSN: 0022-314X
DOI: 10.1016/0022-314x(76)90019-6

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Let \(\mathbf{R}\) be a set of \(r\) distinct nonzero residues modulo a prime \(p\), and suppose that the random variable \(a\) is drawn with the uniform distribution from \(\{1,2, \ldots, p-1\}\). We show for all sets \(\mathbf{R}\) that \((p-2) / 2 r) \leqslant E[\min [a \mathbf{R}]] \leqslant 100