2020 CIME II Problems/Problem 4
Contents
Problem
The probability a randomly chosen positive integer has more digits when written in base than when written in base can be expressed in the form , where and are relatively prime positive integers. Find .
Solution
If a positive integer has more digits in base than base , then for some positive integer . There are positive integers that satisfy this condition for every positive integer . If , will be greater than , so we only need to consider . The number of possible values of is The requested probability is and so the answer is .
Similar Problems
See also
2020 CIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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