2012•Basic Sciences Journal of Textile UniversitiesRequires access
On the mean value properties of the polygonal number residue and its asymptotic formula
Qing Li
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Abstract
For any positive integer m and a fixed positive integer s(s≥3),let c(n) denote the polygonal number residue.That is,for any fixed positive s,c(n) is the smallest nonnegative integer number such that n-c(n) is a polygonal number m[(s-2)m-(s-4)]/2.By using the elementary methods,the mean value properties of the polygonal number residue c(n) and Ω(c(n)) are studied,interesting asymptotic formula are also given.