2018 AIME I Problems/Problem 2
Problem
The number can be written in base as , can be written in base as , and can be written in base as , where . Find the base- representation of .
Solution
We have these equations: . Taking the last two we get . Because otherwise , and , .
Then we know . Taking the first two equations we see that . Combining the two gives . Then we see that .
-gorefeebuddie
See Also
2018 AIME I (Problems • Answer Key • Resources) | ||
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Followed by Problem 3 | |
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