欧几里德引理的错误处理
On the Success of Mishandling Euclid's Lemma
摘要：
我们研究欧几里得引理，如果$p$是一个素数，使$p | ab$，那么$p$除了至少一个$a$或$b$。具体来说，我们认为这个引理的常见误用的数字，不是素数，经常是由本科生。我们表明，随机选择的含义的形式$r |ab \Rightarrow r|a \text{ or } r|b$几乎肯定是假的概率意义上，我们量化了相应的渐近公式。
英文摘要：
We examine Euclid's lemma that if $p$ is a prime number such that $p | ab$, then $p$ divides at least one of $a$ or $b$. Specifically, we consider the common misapplication of this lemma to numbers that are not prime, as is often made by undergraduate students. We show that a randomly chosen implication of the form $r |ab \Rightarrow r|a \text{ or } r|b$ is almost surely false in a probabilistic sense, and we quantify this with a corresponding asymptotic formula.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
