Difference between revisions of "2008 AIME II Problems"

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Let <math>N = 100^2 + 99^2 - 98^2 - 97^2 + 96^2 + \cdots + 4^2 + 3^2 - 2^2 - 1^2</math>, where the additions and subtractions alternate in pairs. Find the remainder when <math>N</math> is divided by <math>1000</math>.
 
Let <math>N = 100^2 + 99^2 - 98^2 - 97^2 + 96^2 + \cdots + 4^2 + 3^2 - 2^2 - 1^2</math>, where the additions and subtractions alternate in pairs. Find the remainder when <math>N</math> is divided by <math>1000</math>.
  
[[2008 AIME II Problems/Problem 15|Solution]]
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[[http://www.artofproblemsolving.com/Wiki/index.php/2008_AIME_II_Problems/Problem_1|Solution]]
  
 
== Problem 2 ==
 
== Problem 2 ==

Revision as of 18:29, 3 April 2008

Problem 1

Let $N = 100^2 + 99^2 - 98^2 - 97^2 + 96^2 + \cdots + 4^2 + 3^2 - 2^2 - 1^2$, where the additions and subtractions alternate in pairs. Find the remainder when $N$ is divided by $1000$.

[[1]]

Problem 2

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Problem 3

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Problem 4

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Problem 5

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Problem 6

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Problem 7

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Problem 8

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Problem 9

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Problem 10

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Problem 11

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Problem 12

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Problem 13

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Problem 14

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Problem 15

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