论文标题
ABC猜想的应用到强大的数字
Applications of the abc conjecture to powerful numbers
论文作者
论文摘要
ABC猜想是数字理论中最著名的未解决问题之一。每个真实$ε> 0 $的猜想要求，即方程式$ a+b = c $ at $ c>（rad（a b c））^{1+ε} $只有有限数量的coprime正整数解决方案。如果是真的，ABC的猜想将暗示许多其他著名的定理和猜想是推论的。在本文中，我们讨论了ABC的猜想，并找到有力数字的新应用程序，这是整数$ n $ $ p^2 |每个Prime $ P $的n $，以便$ p | n $。假设ABC猜想的真相，我们回答了有关该主题的早期论文的几个问题。
The abc conjecture is one of the most famous unsolved problems in number theory. The conjecture claims for each real $ε> 0$ that there are only a finite number of coprime positive integer solutions to the equation $a+b = c$ with $c > (rad(a b c))^{1+ε}$. If true, the abc conjecture would imply many other famous theorems and conjectures as corollaries. In this paper, we discuss the abc conjecture and find new applications to powerful numbers, which are integers $n$ for which $p^2 | n$ for every prime $p$ such that $p | n$. We answer several questions from an earlier paper on this topic, assuming the truth of the abc conjecture.
