2008 AIME II Problems/Problem 4
Problem
There exist unique nonnegative integers and unique integers () with each either or such that Find .
Solution
In base , we find that . In other words,
In order to rewrite as a sum of perfect powers of , we can use the fact that :
The answer is .
Note : Solution by bounding is also possible, namely using the fact that
See also
2008 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
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