The present paper proves that if for a power sum $\alpha$ over $\ZZ$ thelength of the period of the continued fraction for $\sqrt{\alpha(n)}$ isconstant 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 beexpressed by power sums of the same kind.
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机译:本文证明,如果对于幂和$ \ alpha $超过$ \ ZZ $,则$ \ sqrt {\ alpha(n)} $的连续分数的周期的长度对于无限多个偶数(分别为奇数)是恒定的。 n $,然后$ \ sqrt {\ alpha(n)} $允许对所有偶数(分别为奇数)$ n $(有限个除外)进行连续的分数扩展;特别地,对于这样的$ n $,部分商可以用相同种类的幂和来表达。
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