Difference between revisions of "2021 AIME I Problems/Problem 7"
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==Problem== | ==Problem== | ||
| − | + | Find the number of pairs <math>(m,n)</math> of positive integers with <math>1\le m<n\le 30</math> such that there exists a real number <math>x</math> satisfying<cmath>\sin(mx)+\sin(nx)=2.</cmath> | |
==Solution== | ==Solution== | ||
Revision as of 15:47, 11 March 2021
Problem
Find the number of pairs 
of positive integers with 
such that there exists a real number 
satisfying![\[\sin(mx)+\sin(nx)=2.\]](http://latex.artofproblemsolving.com/3/d/c/3dc7189bf3226f56ef411df7b580c6778ace2c72.png)
Solution
See also
| 2021 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
