Mock AIME 2 2006-2007 Problems/Problem 2

Problem

The set $\displaystyle S$ consists of all integers from $\displaystyle 1$ to $\displaystyle 2007,$ inclusive. For how many elements $\displaystyle n$ in $\displaystyle S$ is $\displaystyle f(n) = \frac{2n^3+n^2-n-2}{n^2-1}$ an integer?

f(n) = ((n^2-1)(2n+1) + n - 1)/(n^2-1)

f(n) = (2n+1) + (n-1)/(n^2-1)

f(n) = (2n+1) + 1/(n+1)

1/(n+1) is not an integer for any of the specified n so no solutions and the answer is 000

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Mock AIME 2 2006-2007 Problems/Problem 2

Problem