A note on the q -adic valuation of Olivier Bordellès

Abstract

In this note, we obtain an exact formula for the q -adic valuation of

, where q is an odd prime, allowing us to derive an explicit upper bound which is asymptotically better than the previous bound obtained by Zhao when n is large and

k ⩾ q − 2 $k \geqslant q-2$ k greater than or slanted equals q minus 2

. The key parts are played by the LTE lemma and the use of cyclotomic polynomials.