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On a Question of Buium |
Canad. Math. Bull. 43(2000), 236-238
Published:2000-06-01
Printed: Jun 2000
Printed: Jun 2000
- José Felipe Voloch
Abstract
We prove that $\{(n^p-n)/p\}_p \in \prod_p \mathbf{F}_p$, with $p$
ranging over all primes, is independent of $1$ over the integers,
assuming a conjecture in elementary number theory generalizing
the infinitude of Mersenne primes. This answers a question of
Buium. We also prove a generalization.
| MSC Classifications: | 11A07 - Congruences; primitive roots; residue systems |