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\(\sum \limits_{d \mid n} \mu(d) = [n = 1]\)
\(\mu * I = e\)
\(\sum \limits_{d \mid n} \varphi(d) = n\)
\(\varphi(d) * I = id\)
\(\sum \limits_{d \mid n} d \mu(\frac{n}{d}) = \varphi(n)\)
\(\mu * id = \varphi\)
\(\sum \limits_{d \mid n} \mu(d) = [n = 1]\)
\([\gcd(i, j) = 1] = \sum \limits_{d \mid i, d \mid j}\mu(d)\)
\(\sum\limits_{i = 1}^{n} \sum \limits_{j = 1}^{m} \sum \limits_{d \mid i, d \mid j} \mu(d) = \sum \limits_{d = 1}^{n} \mu(d) \lfloor \frac{n}{d} \rfloor \lfloor \frac{m}{d} \rfloor\)
\(B_t(x) \equiv B_{t - 1}(x)(2 - A(x)B_{t - 1}(x)) \pmod{x^{2^t}}\)
\(f_i(x) = f(x) \frac{w_i}{x - x_i}\)
\(F(x) = f(x)\sum\limits_{i = 0}^n \frac{w_i}{x - x_i} y_i\)
\(P_n(x) = y_i\frac{(x - x2)(x - x3) \cdots (x - x_n)(x - x_{n + 1})}{(x_1 - x_2)(x_1 - x_3)\cdots(x_1 - x_n)(x_1 - x_{n + 1})}\)