this person mjj

useful:

$\text{IMGSE}$图床

$\LaTeX$在线编辑器

$\Huge氵^{\large 夂}_{ \tiny 口}$谷官网

[冬]论编辑器

凸轮边际气$\times2$

集合

$$\begin{aligned}\mathbf{N} & = 自然数\\\mathbf{N^*} & = 正整数\\\mathbf{N_+} & = 正整数\\\mathbf{Z} & = 整数\\\mathbf{Q} & = 有理数\\\mathbf{Q_\pm } & = 正负有理数\\\mathbf{R} & = 实数\\\mathbf{R_\pm } & = 正负实数\\\mathbf{C} & = 虚数\\\mathbf{\oslash } & = 实数\\\end{aligned} $$

好玩的

费马小定理&逆元&分数取$\%$

$$\begin{aligned} \because b^{m-1}&\equiv1\pmod{m}\\ \therefore b^{m-2}&\equiv b^{-1}\pmod{m}\\ ab^{m-2}&\equiv ab^{-1}\pmod{m}\\ ab^{m-2}&\equiv \frac{a}{b}\pmod m\\ \text{if~~~~~~} b&\equiv1\pmod m \end{aligned} $$

各种方程

0

$$a=0$$

1

$$\begin{aligned} ax+b&=0\\ x&=-\frac{b}{a} \end{aligned} $$

2

$$\begin {aligned} ax^2+bx+c&=0\\ \Delta&=b^2-4ac\\ x_1,x_2 &= \frac{-b\pm\sqrt{\Delta}}{2a} \end {aligned} $$

3

$$\begin {aligned} x^3+ax+b&=0\\ \Delta &= \left(\frac{b}{2}\right)^2+\left(\frac{a}{3}\right)^3\\ p,q&=\sqrt[3]{-\left(\frac{b}{2}\right)\pm\sqrt{\Delta}}\\ \omega &= \frac{-1+\sqrt{3}i}{2}\\ x_1 &= p+q\\ x_2 &= \omega p+\omega^2q\\ x_3 &= \omega^2p+\omega q\\ \end {aligned}\\ $$