2022 SSMO Accuracy Round Problems/Problem 10
Problem
Let![\[S=\sum^{\infty}_{k=5}2^{-10k}\dbinom{2k}{10}.\]](http://latex.artofproblemsolving.com/6/e/3/6e3272190c96fe08dc4900c436ec41a317106d8d.png)
Then the value of 
can be expressed as 
, where 
and 
are relatively prime positive integers. Find the largest positive integer 
such that 
.
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