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arXiv · 0712.1080

On the Distribution of Pseudopowers

Sergei V. Konyagin·Carl Pomerance·Igor E. Shparlinski
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Abstract

An $x$-pseudopower to base $g$ is a positive integer which 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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Sergei V. Konyagin, Carl Pomerance, Igor E. Shparlinski. 2007-12-07. On the Distribution of Pseudopowers. https://doi.org/10.4153/cjm-2010-020-4

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