Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 8"
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== 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}} | ||
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| + | ---- | ||
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| + | *[[Mock AIME 2 2006-2007/Problem 7 | Previous Problem]] | ||
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| + | *[[Mock AIME 2 2006-2007/Problem 9 | Next Problem]] | ||
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| + | *[[Mock AIME 2 2006-2007]] | ||
Revision as of 19:48, 22 August 2006
Problem
The positive integers 
satisfy 
and 
for 
. Find the last three digits of 
.
Solution
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