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Search: MSC category 11A07 ( Congruences; primitive roots; residue systems )

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1. CJM 2009 (vol 62 pp. 582)

Konyagin, Sergei V.; Pomerance, Carl; Shparlinski, Igor E.
On the Distribution of Pseudopowers
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 $ple x$. 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.

Categories:11A07, 11L07, 11N36

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