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Does the period length $l(pq)$ of the continued fraction of $\sqrt{pq}$, for $p$ and $q$ primes, follow some type of divisibility property, say $$ l(pq) = c\frac{l(p)}{l(q)} \quad\text{or}\quad c\frac{l(q)}{l(p)}, $$ where $l(p)$ is the period of $\sqrt{p}$ and $c > 0$ is an abosulute absolute constant.

In the previous question, Franz Lemmermeyer mentioned that it depends on the squarefree kernel of the integer.

Note: The theorem on the upper bound of the length of period of continued fraction implies that $l(\ \cdot\ )$ is not multiplicative.

Thank you, Jerald Jetson.
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Does the period length $l(pq)$ of the continued fraction of the radical of a product (pq)^.5, p $\sqrt{pq}$, for $p$ and q $q$ primes, follows follow some type of divisivility divisibility property, say $$ l(pq) = c*l(p)/l(q) or c*l(q)/l(p)c\frac{l(p)}{l(q)} \quad\text{or}\quad c\frac{l(q)}{l(p)}, $$ where l(p) $l(p)$ is the period of (p)^.5 $\sqrt{p}$ and $c > 0 0$ is a an abosulute constant.

On a

In the previous question, Franz Lemmermeyer mentioned that it depends on the kernal squarefree kernel of the integer.

Note: The theorem on the upper bound of the length of period of the continued fraction implies that it $l(\ \cdot\ )$ is not multiplicative.

Thank you, Jerald Jetson.
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Periods of Continued Fractions

Does the period of the continued fraction of the radical of a product (pq)^.5, p and q primes, follows some type of divisivility property, say

l(pq) = c*l(p)/l(q) or c*l(q)/l(p),

where l(p) is the period of (p)^.5 and c > 0 is a constant.

On a previous question, Franz Lemmermeyer mentioned that it depends on the kernal of the integer.

Note: The theorem on the upper bound of the period of the continued fraction implies that it is not multiplicative.

Thank you, Jerald Jetson.