问题

Questions in category: 初等数论 (Elementary Number Theory).

Farey 序列的性质

Posted by haifeng on 2011-08-10 15:02:10 last update 2015-04-23 09:54:03 | Answers (0) | 收藏

$F_{n-1}\subset F_n$
$|F_n|=|F_{n-1}|+\varphi(n)$
设 $\frac{p}{q},\frac{p'}{q'},\frac{p''}{q''}$ 是 $F_n$ 中连续的三个分数. 则有 \[ p''=\lfloor\frac{q+n}{q'}\rfloor p'-p,\quad q''=\lfloor\frac{q+n}{q'}\rfloor q'-q. \]