Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 2"
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== Problem == | == Problem == | ||
| − | The [[set]] <math> | + | The [[set]] <math>S</math> consists of all [[integer]]s from <math>1</math> to <math>2007</math>, inclusive. For how many [[element]]s <math>n</math> in <math>S</math> is <math>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>. | <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>. | ||
| − | + | ==See Also== | |
| − | + | {{Mock AIME box|year=2006-2007|n=2|num-b=1|num-a=3}} | |
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Latest revision as of 09:49, 4 April 2012
Problem
The set 
consists of all integers from 
to 
, inclusive. For how many elements 
in is 
an integer?
Solution
. So in fact, there are 0 such elements of .
See Also
| Mock AIME 2 2006-2007 (Problems, Source) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
