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

(Problem)
m
Line 1: Line 1:
 
== Problem ==
 
== Problem ==
 
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>.
 
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>.
 +
==Solution==
 +
{{solution}}
 +
 +
----
 +
 +
*[[Mock AIME 2 2006-2007/Problem 7 | Previous Problem]]
 +
 +
*[[Mock AIME 2 2006-2007/Problem 9 | Next Problem]]
 +
 +
*[[Mock AIME 2 2006-2007]]

Revision as of 19:48, 22 August 2006

Problem

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

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.


Invalid username
Login to AoPS