Affiliation:
1. Department of Mathematics, Lehman College (CUNY), Bronx, New York 10468, USA
Abstract
Define the height function h(a) = min {k + (ka mod p) : k = 1, 2, …, p - 1} for a ∈ {0, 1, …, p - 1.} It is proved that the height has peaks at p, (p + 1)/2, and (p + c)/3, that these peaks occur at a = [p/3], (p - 3)/2, (p - 1)/2, [2p/3], p - 3, p - 2, and p - 1, and that h(a) ≤ p/3 for all other values of a.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
2 articles.
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1. Addictive Number Theory;Additive Number Theory;2010
2. Nathanson heights in finite vector spaces;Journal of Number Theory;2008-09