2025 SSMO Team Round Problems/Problem 12
Problem
Let 
for all nonnegative integers 
. Let ![\[\sum_{k=0}^\infty\frac{\lfloor a_k\rfloor}{10^k}=\frac{m}{n},\]](http://latex.artofproblemsolving.com/a/7/1/a71cc89701b5c2a7a39fe3e047cd5f92022333cf.png)
where 
and are relatively prime positive integers. Find 
.
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