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GEOMETRIC PROPERTIES OF POINTS ON MODULAR HYPERBOLAS

KEVIN FORD, MIZAN R. KHAN and IGOR E. SHPARLINSKI
Proceedings of the American Mathematical Society
Vol. 138, No. 12 (DECEMBER 2010), pp. 4177-4185
Stable URL: http://www.jstor.org/stable/41059155
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
GEOMETRIC PROPERTIES OF POINTS ON MODULAR HYPERBOLAS
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Abstract

Given an integer n > 2, let Hn be the set H n = {(a, b) : ab ≡ 1 (mod n ), 1 < a,b < n - 1} and let M(n) be the maximal difference b — a for (a,b) ∈ H n . We prove that for almost all n, n — M(n) = O (n½⁺ ° (1) ) We also improve some previously known upper and lower bounds on the number of vertices of the convex closure Of H n .

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