How do you know that 4/11 is a reapeating decimal
2 answers:
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Suppose we choose 
and 
. Then
Now suppose we choose
such that
where we pick the solution for this system such that
. Then we find
Note that you can always find a solution to the system above that satisfies as long as 
. What this means is that you can always find the value of 
as a (constant) function of 
.
Now suppose we choose
where we pick the solution for this system such that
Note that you can always find a solution to the system above that satisfies