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 integers from <math>\displaystyle 1</math> to <math>\displaystyle 2007,</math> inclusive. For how many elements <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? | The set <math>\displaystyle S</math> consists of all integers from <math>\displaystyle 1</math> to <math>\displaystyle 2007,</math> inclusive. For how many elements <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? | ||
| + | |||
| + | 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 | ||
Revision as of 13:04, 9 August 2006
Problem
The set 
consists of all integers from 
to 
inclusive. For how many elements 
in is 
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
