Fixed Points for Discrete Logarithms
نویسندگان
چکیده
Abstract: We establish a conjecture of Brizolis that for every prime p > 3 there is a primitive root r and an integer t in the interval [1, p− 1] with logr t = t. Here, logr is the discrete logarithm function to the base r for the cyclic group (Z/pZ)×. Tools include a numerically explicit version of the Pólya–Vinogradov inequality for the sum of values of a Dirichlet character on an interval, some combinatorial sieving techniques, plus an exhaustive search over small cases.
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تاریخ انتشار 2010