Difference between revisions of "2018 AIME I Problems"
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==Problem 11== | ==Problem 11== | ||
+ | Find the least positive integer <math>n</math> such that when <math>3^n</math> is written in base <math>143</math>, its two right-most digits in base <math>143</math> are <math>01</math>. | ||
Revision as of 15:59, 7 March 2018
2018 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
Instructions
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1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |
Contents
[hide]Problem 1
Let be the number of ordered pairs of integers with and such that the polynomial can be factored into the product of two (not necessarily distinct) linear factors with integer coefficients. Find the remainder when is divided by .
Problem 2
Problem 3
Kathy has
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Find the number of four-element subsets of with the property that two distinct elements of a subset have a sum of , and two distinct elements of a subset have a sum of . For example, and are two such subsets.
Problem 10
The wheel shown below consists of two circles and five spokes, with a label at each point where a spoke meets a circle. A bug walks along the wheel, starting at point
Problem 11
Find the least positive integer such that when is written in base , its two right-most digits in base are .
Problem 12
Problem 13
Problem 14
Problem 15
2018 AIME I (Problems • Answer Key • Resources) | ||
Preceded by 2017 AIME II |
Followed by 2018 AIME II | |
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All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.