数论中两个问题的复杂性方法
Complexities Approach to Two Problems In Number Theory
摘要：
利用Kolmogorov复杂性，我们用不同的方法解决了两个数论问题，一个是Maxim Kontsevich和Don Bernard Zagier的问题3 \emph{Exhibit at least one number which does not belong to} $ \mathcal{P}$（周期数），另一个是关于超越数的连分数展开式的有界系数的存在性问题，从而为解决非逻辑学科中的数学问题提供了一种新的途径.我们证明了资源受限的Kolmogorov复杂性和计算复杂性至少可以为非传统或逻辑学科中的数学问题提供提示或原则。
英文摘要：
By Kolmogorov Complexity,two number-theoretic problems are solved in different way than before,one problem is Maxim Kontsevich and Don Bernard Zagier's Problem 3 \emph{Exhibit at least one number which does not belong to} $ \mathcal{P}$ (period number) in their paper,another is the problem about existence of bounded coefficients of continued fraction expansion of transcendental number.Thus we show a new approach to mathematical problems in the non-logical discipline.Futhermore,we show that resource-bounded Kolmogorov Complexity and computational complexity can at least provide tips or principles to mathematical problems in the non-traditional or logical discipline.
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