2010 AIME I Problems/Problem 2
Contents
[hide]Problem
Find the remainder when is divided by .
Solution
Note that (see modular arithmetic). That is a total of integers, so all those integers multiplied out are congruent to . Thus, the entire expression is congruent to .
Solution 2
The expression also equals . To find its modular 1,000, remove all terms from 1,000 and after. Then the expression becomes
By maxamc
Video Solution by OmegaLearn
https://youtu.be/orrw4VydBTk?t=140
~ pi_is_3.14
Video Solution
https://www.youtube.com/watch?v=-GD-wvY1ADE&t=78s
Video Solution by WhyMath
~savannahsolver
See Also
2010 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
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