2013 AMC 10A Problems/Problem 19
Contents
[hide]Problem
In base , the number ends in the digit . In base , on the other hand, the same number is written as and ends in the digit . For how many positive integers does the base--representation of end in the digit ?
Solution
We want the integers such that is a factor of . Since , it has factors. Since cannot equal or , as these cannot have the digit in their base representations, our answer is
Video Solution by SpreadTheMathLove
https://www.youtube.com/watch?v=msGdQB7_-50
Video Solution by OmegaLearn
https://youtu.be/ZhAZ1oPe5Ds?t=4366
~ pi_is_3.14
See Also
2013 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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All AMC 10 Problems and Solutions |
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