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On the Distribution of Pseudopowers
Published online by Cambridge University Press: 20 November 2018
Abstract
An $x$-pseudopower to base $g$ is a positive integer that is not a power of $g$, yet is so modulo $p$ for all primes $p\,\le \,x$. We improve an upper bound for the least such number, due to E. Bach, R. Lukes, J. Shallit, and H. C. Williams. The method is based on a combination of some bounds of exponential sums with new results about the average behaviour of the multiplicative order of $g$ modulo prime numbers.
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- Copyright © Canadian Mathematical Society 2010
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