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On The Primitive Numbers Of Power P And Its Mean Value Properties

Liping Ding

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Abstract

Let p be a prime, n be any fixed positive integer. Sp(n) denotes the smallest positive integer such that Sp(n)! is divisible by pn. In this paper, we study the mean value properties of Sp(n) for p, and give a sharp asymptotic formula for it.

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What this paper is about

Let p be a prime, n be any fixed positive integer. Sp(n) denotes the smallest positive integer such that Sp(n)! is divisible by pn. In this paper, we study the mean value properties of Sp(n) for p, and give a sharp asymptotic formula for it.

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Available abstract

Let p be a prime, n be any fixed positive integer. Sp(n) denotes the smallest positive integer such that Sp(n)! is divisible by pn. In this paper, we study the mean value properties of Sp(n) for p, and give a sharp asymptotic formula for it.

Key concepts: Integer (computer science), Mathematics, Value (mathematics), Combinatorics, Asymptotic formula, Mean value, Prime (order theory), Prime power

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