Difference between revisions of "2025 AIME I Problems/Problem 1"
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Find the sum of all integer bases <math>b>9</math> for which <math>17_b</math> is a divisor of <math>97_b.</math> | Find the sum of all integer bases <math>b>9</math> for which <math>17_b</math> is a divisor of <math>97_b.</math> | ||
==Solution 1== | ==Solution 1== | ||
| − | We have, <math>b + 7 \mid 9b + 7</math> meaning <math>b + 7 \mid -56</math> so taking divisors of 56 under bounds to find <math>b = 49, 21</math> meaning our answer is <math>49+21=\boxed{070}.</math> | + | We have, <math>b + 7 \mid 9b + 7</math> meaning <math>b + 7 \mid -56</math> so taking divisors of <math>56</math> under bounds to find <math>b = 49, 21</math> meaning our answer is <math>49+21=\boxed{070}.</math> |
Revision as of 16:57, 13 February 2025
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 
