On Hexagon Number Part Residue of a Positive Integer
To study the hexagon number part residue function \( a(n) \) and to generalize it. For any positive integer \( n, \) \( a(n) \) is the smallest nonnegative integer such that \( n - a(n) \) is a hexagon number. Based on this definition, the asymptotic properties of this function and some hybrid functions are studied using the elementary method, the asymptotic formulae are obtained, thus enriching the study and application of this function.
KeywordsThe hexagon number part residue Mean value Asymptotic formula
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