Difference between revisions of "2010 AIME I Problems/Problem 2"
(credit to gaussintraining) |
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Revision as of 13:15, 17 March 2010
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
.
See also
2010 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |