Difference between revisions of "2014 AMC 12B Problems/Problem 23"
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<cmath>\left(\frac{62}{2}+1 \right)^2 = 32^2 = \boxed{\textbf{(C)}\ 1024}</cmath> | <cmath>\left(\frac{62}{2}+1 \right)^2 = 32^2 = \boxed{\textbf{(C)}\ 1024}</cmath> | ||
+ | == See also == | ||
{{AMC12 box|year=2014|ab=B|num-b=22|num-a=24}} | {{AMC12 box|year=2014|ab=B|num-b=22|num-a=24}} | ||
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Revision as of 13:26, 22 February 2014
Problem
The number 2017 is prime. Let . What is the remainder when is divided by 2017?
Solution
Note that . We have for Therefore This is simply an alternating series of triangular numbers that goes like this: After finding the first few sums of the series, it becomes apparent that and Obviously, falls in the second category, so our desired value is
See also
2014 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Problem 24 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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