关于五边形数的余数及其渐进公式

On the Pentagon Number Residue and Its Asymptotic Formula

对于任意的正整数n,设f(n)表示n的五边形数的余数,即f(n)是使得n-f(n)为一五边形数(m(m-1))/2的最小非负整数.运用初等和分析的方法研究了五边形数的余数列{f(n)}(n=1,2,…)的渐进性质,并给出了不同类型的渐进公式.

For any positive n, let f（n） denote the pentagon number residue, that is,for any fixed positive n, f（n） is the smallest nonnegative integer number such that n-f （n） is a pentagon number m（3m-1）/2. By using the elementary and analytic methods, the asymptotic properties of the pentagon number sequence are studied; different kinds of asymptotic formula are also given.