2025 AIME I Problems/Problem 1
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 | |
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