171. 证明 $\sum_{i=1}^{n}\frac{1}{i}\ (n>1)$ 不是整数.
Posted by haifeng on 2011-05-04 13:00:01 last update 0000-00-00 00:00:00 | Answers (0) | 收藏
Posted by haifeng on 2011-05-04 13:00:01 last update 0000-00-00 00:00:00 | Answers (0) | 收藏
Posted by haifeng on 2011-04-28 23:13:28 last update 2021-05-18 12:55:35 | Answers (0) | 收藏
若 $ax_0+by_0$ 是形如 $ax+by$ ($x,y$ 是任意整数, $a,b$ 是两个不全为零的整数)的数中的最小正数, 则 \[ (ax_0+by_0)\mid (ax+by), \] 其中 $x,y$ 是任何整数. 即
\[\min\{ax+by\mid ax+by>0, x,y\in\mathbb{Z}, a^2+b^2>0\}\mid(ax+by)\]
Posted by haifeng on 2011-04-28 22:33:34 last update 0000-00-00 00:00:00 | Answers (1) | 收藏