Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 2"
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== Problem == | == Problem == | ||
| − | The set <math>\displaystyle S</math> consists of all | + | The [[set]] <math>\displaystyle S</math> consists of all [[integer]]s from <math>\displaystyle 1</math> to <math>\displaystyle 2007</math>, inclusive. For how many [[element]]s <math>\displaystyle n</math> in <math>\displaystyle S</math> is <math>\displaystyle f(n) = \frac{2n^3+n^2-n-2}{n^2-1}</math> an integer? |
==Solution== | ==Solution== | ||
| − | {{ | + | <math>f(n) = \frac{2n^3+n^2-n-2}{n^2-1} = \frac{(n - 1)(2n^2 + 3n + 2)}{(n - 1)(n + 1)} = \frac{2n^2 + 3n + 2}{n + 1} = 2n + 1 + \frac1{n+1}</math>. So in fact, there are 0 such elements of <math>S</math>. |
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consists of all 
to 
, inclusive. For how many 
in 
an integer?
. So in fact, there are 0 such elements of 
.
