Results and estimates on pseudopowers

  title={Results and estimates on pseudopowers},
  author={Eric Bach and Richard F. Lukes and Jeffrey Shallit and Hugh C. Williams},
  journal={Math. Comput.},
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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