On the Distribution of Pseudopowers

Details On the Distribution of Pseudopowers On the Distribution of Pseudopowers

2007-12-07

arxiv.org/abs/0712.1080v1

Mathematics

Number Theory

Scientific paper

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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