论文标题
关于P-ADIC的算法的周期性持续分数
On the periodicity of an algorithm for p-adic continued fractions
论文作者
论文摘要
在本文中，我们研究了一种算法在p-adic数字$ \ mathbb {q} _p $领域中生成持续分数的属性。首先，我们获得了Galois定理的经典持续分数的类似物。然后，我们研究了平方根周期性膨胀的预科长度。最后，我们证明，在$ \ mathbb {q} _p $中具有无限的整数平方根，它们具有周期性扩展，其中有四个长度为4，解决了Browkin留下的空旷问题。
In this paper we study the properties of an algorithm for generating continued fractions in the field of p-adic numbers $\mathbb{Q}_p$. First of all, we obtain an analogue of the Galois' Theorem for classical continued fractions. Then, we investigate the length of the preperiod for periodic expansions of square roots. Finally, we prove that there exist infinitely many square roots of integers in $\mathbb{Q}_p$ that have a periodic expansion with period of length four, solving an open problem left by Browkin.
