On the Distribution of Pseudopowers
Number Theory
2019-08-15 v1
Abstract
An -pseudopower to base is a positive integer which is not a power of yet is so modulo for all primes . 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 modulo prime numbers.
Keywords
Cite
@article{arxiv.0712.1080,
title = {On the Distribution of Pseudopowers},
author = {Sergei V. Konyagin and Carl Pomerance and Igor E. Shparlinski},
journal= {arXiv preprint arXiv:0712.1080},
year = {2019}
}