Difference between revisions of "2024 AIME I Problems/Problem 13"
m (→Solution 2) |
Tensorguy666 (talk | contribs) (→Solution 3) |
||
Line 62: | Line 62: | ||
We work in the ring | We work in the ring | ||
<cmath>\sqrt[4]{-1}=\pm\sqrt{\frac12}\pm\sqrt{-\frac12}.</cmath> | <cmath>\sqrt[4]{-1}=\pm\sqrt{\frac12}\pm\sqrt{-\frac12}.</cmath> | ||
− | Since | + | Since |
==Video Solution 1 by OmegaLearn.org== | ==Video Solution 1 by OmegaLearn.org== |
Revision as of 12:02, 5 February 2024
Contents
[hide]Problem
Let be the least prime number for which there exists a positive integer such that is divisible by . Find the least positive integer such that is divisible by .
Solution
From there, we could get
By doing binomial expansion bash, the four smallest in this case are , yielding
~Bluesoul
Solution 2
If
For integer
If
If
If
In conclusion, the smallest possible
Solution by Quantum-Phantom
Solution 3
We work in the ring
Video Solution 1 by OmegaLearn.org
Video Solution 2
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See also
2024 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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.