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abc conjecture

abc 猜想

本站译名 代数数论与算术几何 义项编号TS-1665

英文别名
ABC conjecture

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The Arithmetic of Elliptic Curves 封面

《The Arithmetic of Elliptic Curves》 · 第 258 页 · Chapter VIII,Section 11「Szpiro's Conjecture and ABC」,Conjecture 11.4

Szpiro’s conjecture is closely related to the ABC conjecture that was proposed by Masser and Oesterlé in 1985. The ABC Conjecture 11.4. (Masser–Oesterlé) For every $\epsilon>0$ there exists a constant $\kappa_\epsilon$ such that for all nonzero integers $A,B,C\in\mathbb Z$ satisfying $A+B=C$ and $\gcd(A,B,C)=1$, we have $\max\{|A|,|B|,|C|\}\leq\kappa_\epsilon\left(\prod_{p\mid ABC}p\right)^{1+\epsilon}$.

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