# Difference between revisions of "2005 AIME II Problems/Problem 11"

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== See Also == | == See Also == | ||

+ | *[[2005 AIME II Problems/Problem 10| Previous problem]] | ||

+ | *[[2005 AIME II Problems/Problem 12| Next problem]] | ||

* [[2005 AIME II Problems]] | * [[2005 AIME II Problems]] | ||

[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] |

## Revision as of 20:07, 7 September 2006

## Problem

Let be a positive integer, and let be a sequence of integers such that and for Find

## Solution

For , we have

.

Thus the product is a monovariant: it decreases by 3 each time increases by 1. Since for we have , so when , will be zero for the first time, which implies that , our answer.