# Results and estimates on pseudopowers

@article{Bach1996ResultsAE, title={Results and estimates on pseudopowers}, author={Eric Bach and Richard F. Lukes and Jeffrey Shallit and Hugh C. Williams}, journal={Math. Comput.}, year={1996}, volume={65}, pages={1737-1747} }

- Published 1996 in Math. Comput.
DOI:10.1090/S0025-5718-96-00762-4

Let n be a positive integer. We say n looks like a power of 2 modulo a prime p if there exists an integer ep ≥ 0 such that n ≡ 2ep (mod p). First, we provide a simple proof of the fact that a positive integer which looks like a power of 2 modulo all but finitely many primes is in fact a power of 2. Next, we define an x-pseudopower of the base 2 to be a positive integer n that is not a power of 2, but looks like a power of 2 modulo all primes p ≤ x. Let P2(x) denote the least such n. We give an… CONTINUE READING

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