Difference between revisions of "2023 SSMO Team Round Problems/Problem 12"
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Latest revision as of 22:25, 15 December 2023
Problem
Let 
be the set of rationals of the form 
for nonnegative 
and 
. Define the function 
such that, for 
such is minimal, we have that
![\[f\left(\frac{a}{2^b}\right) = \begin{cases} 1 & b = 0 \\ f\left(\frac{a-1}{2^b}\right) + f\left(\frac{a+1}{2^b}\right) & b \ne 0 \\ \end{cases}\]](http://latex.artofproblemsolving.com/d/6/8/d68e4a0be5eb87b2f25c76e0b6a55794b057c384.png)
Suppose
![\[\sum_{i=0}^{2^{10} - 1} \frac{f\left(\frac{i+1}{2^{10}}\right)}{f\left(\frac{i}{2^{10}}\right)}\]](http://latex.artofproblemsolving.com/6/0/7/6076f14051ed7c9119ecb8edf8e504782a7345bf.png)
equals 
. Find 
.
