On the distribution of pseudopowers

Sergei V. Konyagin, Carl Pomerance, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 ≤ 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.

Original languageEnglish
Pages (from-to)582-594
Number of pages13
JournalCanadian Journal of Mathematics
Issue number3
Publication statusPublished - Jun 2010


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