论文标题
两个受限制的ABC猜想
Two Restricted ABC Conjectures
论文作者
论文摘要
埃伦伯格（Ellenberg）证明，如果以$ a+a+b = c $闻名，ABC的猜想将遵循，以便某些整数〜$ d $ $ d \ d \ mid abc $。 Mochizuki证明了具有相反限制的定理，如果以ABC总和不可分割的ABC总和而闻名。我们证明了通用数字字段的两个定理。
Ellenberg proved that the abc conjecture would follow if this conjecture were known for sums $a+b=c$ such that $D\mid abc$ for some integer~$D$. Mochizuki proved a theorem with an opposite restriction, that the full abc conjecture would follow if it were known for abc sums that are not highly divisible. We prove both theorems for general number fields.
