  The present paper proves that if for a power sum $\alpha$ over $\ZZ$ the
length of the period of the continued fraction for $\sqrt{\alpha(n)}$ is
constant for infinitely many even (resp. odd) $n$, then $\sqrt{\alpha(n)}$
admits a functional continued fraction expansion for all even (resp. odd) $n$,
except finitely many; in particular, for such $n$, the partial quotients can be
expressed by power sums of the same kind.

Number Theory