论文标题
罗斯的定理意味着特殊情况的ABC猜想的版本较弱
Roth's Theorem implies a Weakened Version of the ABC Conjecture for Special Cases
论文作者
论文摘要
Enrico Bombieri证明了ABC的猜想意味着1994年罗斯定理。本文涉及另一个方向。在利用Bombieri和van der Poorten的明确公式，用于代数数字的常规持续分数的系数，我们证明Roth的定理意味着在某些与根有关的情况下，ABC猜想的非效率较弱。
Enrico Bombieri proved that the ABC Conjecture implies Roth's theorem in 1994. This paper concerns the other direction. In making use of Bombieri's and Van der Poorten's explicit formula for the coefficients of the regular continued fractions of algebraic numbers, we prove that Roth's theorem implies a weakened non-effective version of the ABC Conjecture in certain cases relating to roots.
