Proposition Suppose that
has an eventually periodic continued fraction expansion. Then is a quadratic irrational.
Proof. We first show this when
Since
Since
If
Clearly
Note,
Since
◻︎
Proposition Suppose that
has an eventually periodic continued fraction expansion. Then is a quadratic irrational.
Proof. We first show this when
Since
Since
If
Clearly
Note,
Since
◻︎
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