Difference between revisions of "2023 AMC 12A Problems/Problem 22"
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| − | + | ==Problem== | |
| + | Let <math>f</math> be the unique function defined on the positive integers such that <cmath>\sum_{d\mid n}d\cdot f\left(\frac{n}{d}\right)=1</cmath> for all positive integers <math>n</math>. What is <math>f(2023)</math>? | ||
| − | - | + | <math>\textbf{(A)}~-1536\qquad\textbf{(B)}~96\qquad\textbf{(C)}~108\qquad\textbf{(D)}~116\qquad\textbf{(E)}~144</math> |
| + | |||
| + | ==Video Solution by MOP 2024== | ||
| + | https://YouTube.com/watch?v=gdhVqdRhMsQ | ||
| + | |||
| + | ==See also== | ||
| + | {{AMC12 box|ab=A|year=2023|num-b=22|num-a=24}} | ||
| + | |||
| + | [[Category:Intermediate Number Theory Problems]] | ||
| + | {{MAA Notice}} | ||
Revision as of 14:47, 9 November 2023
Problem
Let 
be the unique function defined on the positive integers such that ![\[\sum_{d\mid n}d\cdot f\left(\frac{n}{d}\right)=1\]](http://latex.artofproblemsolving.com/b/5/7/b5732e957114ff62dabd6b1f9c816210038356c0.png)
for all positive integers 
. What is 
?
Video Solution by MOP 2024
https://YouTube.com/watch?v=gdhVqdRhMsQ
See also
| 2023 AMC 12A (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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
