Fixed Points for Discrete Logarithms

: 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 P´olya–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.

• Type: Conference
• Year: 2010
• Where: ANTS
• Authors: Mariana Levin, Carl Pomerance, K. Soundararajan
• Keywords: Algorithms, ANTS 2010, Combinatorial Sieving Techniques, Discrete Logarithm Function, Primitive Root