# Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 8"

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− | The positive integers <math>\displaystyle x_1, x_2, ... , x_7</math> satisfy <math>\displaystyle x_6 = 144</math> and <math>\displaystyle x_{n+3} = x_{n+2}(x_{n+1}+x_n)</math> for <math>\displaystyle n = 1, 2, 3, 4</math>. Find the last three digits of <math>x_7</math>. | + | The positive integers <math>\displaystyle x_1, x_2, ... , x_7</math> satisfy <math>\displaystyle x_6 = 144</math> and <math>\displaystyle x_{n+3} = x_{n+2}(x_{n+1}+x_n)</math> for <math>\displaystyle n = 1, 2, 3, 4</math>. Find the last three digits of <math>\displaystyle x_7</math>. |

## Revision as of 01:13, 25 July 2006

## Problem

The positive integers satisfy and for . Find the last three digits of .