Definition:Periodic Continued Fraction/Purely Periodic

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Definition

A periodic continued fraction is a purely periodic continued fraction if its partial quotients are of the form:

$\left[{\left \langle{s_1, s_2, \ldots, s_n}\right \rangle}\right]$

That is, all of its partial quotients form a block which repeats itself indefinitely.


Cycle

The repeating block in a periodic (or purely periodic) continued fraction $F$ is called the cycle of $F$.