Difference between revisions of "2000 AIME II Problems/Problem 1"
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~ [https://artofproblemsolving.com/wiki/index.php/User:Cxsmi cxsmi] | ~ [https://artofproblemsolving.com/wiki/index.php/User:Cxsmi cxsmi] | ||
− | == | + | == Video Solution by Pi Academy == |
https://youtu.be/ucn9yfcu1QY?si=r3ebuzJNd2uAq0kV | https://youtu.be/ucn9yfcu1QY?si=r3ebuzJNd2uAq0kV | ||
Latest revision as of 20:04, 9 October 2024
Contents
Problem
The number
can be written as where and are relatively prime positive integers. Find .
Solution
Solution 1
Therefore,
Solution 2
Alternatively, we could've noted that, because
Therefore our answer is .
Solution 3
We know that and , and by base of change formula, . Lastly, notice for all bases.
~
Solution 4
~ cxsmi
Video Solution by Pi Academy
https://youtu.be/ucn9yfcu1QY?si=r3ebuzJNd2uAq0kV
~ Pi Academy
2000 AIME II (Problems • Answer Key • Resources) | ||
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