Equations and Inequalities Involving vp(n!)

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Hassani, Mehdi (2004) Equations and Inequalities Involving vp(n!). Research report collection, 7 (4).


In this paper we study vp(n!), the greatest power of prime p in factorization of n!. We find some lower and upper bounds for vp(n!), and we show that vp(n!) = (n/p−1) + O(ln n). By using above mentioned bounds, we study the equation vp(n!) = v for a fixed positive integer v. Also, we study the triangle inequality about vp(n!), and show that the inequality pvp(n!) > qvq(n!) holds for primes p < q and sufficiently large values of n.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/18061
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords factorial function, prime number, inequality
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