1993 AHSME Problems/Problem 30
Problem
Given , let for all integers . For how many is it true that ?
Solution
We are going to look at this problem in binary.
If , then which means that and so
If then which means that .
Using the same logic, we notice that this sequence cycles and that since we notice that .
We have possibilities for each of to but we can't have so we have
-mathman523
See also
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