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On Rational Functions Representing All Residues Mod P

โœ Scribed by Mordell, L. J.


Book ID
120097529
Publisher
Oxford University Press
Year
1972
Tongue
English
Weight
63 KB
Volume
s2-5
Category
Article
ISSN
0024-6107

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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