论文标题
$ p $ - 亚种的非平凡的下限
Nontrivial lower bounds for the $p$-adic valuations of some type of rational numbers
论文作者
论文摘要
在本文中，我们将证明某种类型的合理数字的$ p $ -ADIC估值（其中$ p $是给定的质量数）异常大。这概括了作者和A. dubickas的最新结果，这两者都与特殊情况$ p = 2 $有关。获得我们主要结果的关键点是，从上方不受限制的有理数字的$ p $ addic估值是不受限制的。我们将通过三种不同的方法确认这一事实。前两个是基本的，而第三个则依靠$ p $ -ADIC分析。
In this paper, we will show that the $p$-adic valuation (where $p$ is a given prime number) of some type of rational numbers is unusually large. This generalizes the very recent results by the author and by A. Dubickas, which are both related to the special case $p = 2$. The crucial point for obtaining our main result is the fact that the $p$-adic valuation of the rational numbers in question is unbounded from above. We will confirm this fact by three different methods; the first two are elementary while the third one leans on the $p$-adic analysis.
