Factorials and powers, a minimality result

2021/06/03 by Radford, David E.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2106.02002

Abstract

Let a > 1. Then aⁿ < n! for some positive integer n. We show that the smallest such n is one of a pair of possibilities, or is one possibility, which we show how to calculate. There are three interesting numerical sequences which play a central role in our arguments. This paper is based on the improvement on Sterling's approximation of factorials due to Robbins \citeRobbins and results of \citeRadford

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