AMC 10A/12A 2024 (Problem 19/12)
The first three terms of a geometric sequence are the integers , , and , where . What is the sum of the digits of the least possible value of ?
To rigorously find the minimum and prove that it is indeed the minimum, you can use casework.
Use casework based on the power of in .
Case 1:
Case 2:
For the remaining cases, if we write down the positive divisors of first, then it will be faster to find the minimum in each case.
Positive divisors of
The number of positive divisors for checking to not miss any of the divisors.
The number of positive divisors for checking to not miss any of the divisors.
So is the least value greater than .
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(E) 21