Difference between revisions of "2024 AIME I Problems/Problem 13"
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==Video Solution 1 by OmegaLearn.org== | ==Video Solution 1 by OmegaLearn.org== | ||
https://youtube/UyoCHBeII6g | https://youtube/UyoCHBeII6g | ||
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+ | ==Video Solution 2== | ||
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+ | https://youtu.be/F3pezlR5WHc | ||
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+ | ~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com) | ||
==See also== | ==See also== |
Revision as of 00:26, 4 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
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.