Difference between revisions of "2025 AIME I Problems/Problem 1"
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Revision as of 19:28, 13 February 2025
Contents
Problem
Find the sum of all integer bases 
for which 
is a divisor of 
Solution 1
We have, 
meaning 
so taking divisors of 
under bounds to find 
meaning our answer is 
Solution 2
This means that 
where 
is a natural number. Rearranging we get 
. Since , 
. Thus the answer is 
See also
| 2025 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by First Problem |
Followed by Problem 2 | |
| 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. 
