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# On a Question of Buium

Published:2000-06-01
Printed: Jun 2000
• José Felipe Voloch
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## 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