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AIME II #1 2008

American Mathematics Contest & American Invitational Mathematics Examination. See for more information
Note:USAMO/IMO-level questions need to go in the Olympiad section.
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AIME II #1 2008

Postby stupidityismygam » Thu Apr 03, 2008 6:49 pm

Let [unparseable or potentially dangerous latex formula] where the additions and subtractions alternate in pairs. Find the remainder when [unparseable or potentially dangerous latex formula] is divided by [unparseable or potentially dangerous latex formula]
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Re: AIME II #1 2008

Postby Michael T » Thu Apr 03, 2008 6:55 pm

Pair the squares up with differences of two...
[unparseable or potentially dangerous latex formula]
Difference of two squares is (difference) * (sum), and the difference between all of our squares is two, so we factor.
[unparseable or potentially dangerous latex formula]
That sum is 5050 (I have this memorized for some reason), and multiplied by two it is then 10100. Remainder is therefore 100.
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