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s(n) = \frac16 n^3 - \frac12 n^2 + \frac13 n is integer when n is integer

Source: Norwegian Mathematical Olympiad 2008 - Abel Competition p1

September 5, 2019
number theorydivisibleInteger

Problem Statement

Let s(n)=16n3−12n2+13ns(n) = \frac16 n^3 - \frac12 n^2 + \frac13 n. (a) Show that s(n)s(n) is an integer whenever nn is an integer. (b) How many integers nn with 0<n≤20080 < n \le 2008 are such that s(n)s(n) is divisible by 44?
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