Difference between revisions of "Mock AIME 3 Pre 2005 Problems/Problem 10"
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| − | + | ==Problem== | |
| − | + | <math>\{A_n\}_{n \ge 1}</math> is a sequence of positive integers such that | |
<math>a_{n} = 2a_{n-1} + n^2</math> | <math>a_{n} = 2a_{n-1} + n^2</math> | ||
for all integers <math>n > 1</math>. Compute the remainder obtained when <math>a_{2004}</math> is divided by <math>1000</math> if <math>a_1 = 1</math>. | for all integers <math>n > 1</math>. Compute the remainder obtained when <math>a_{2004}</math> is divided by <math>1000</math> if <math>a_1 = 1</math>. | ||
| + | |||
| + | ==Solution== | ||
| + | {{solution}} | ||
| + | |||
| + | ==See also== | ||
Revision as of 07:31, 14 February 2008
Problem
is a sequence of positive integers such that
for all integers 
. Compute the remainder obtained when 
is divided by 
if 
.
Solution
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