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1: 28.2 Definitions and Basic Properties
The general solution of (28.2.16) is $\nu=\pm\widehat{\nu}+2n$, where $n\in\mathbb{Z}$. …
28.2.23 $a_{n}\left(0\right)=n^{2},$ $n=0,1,2,\dots$,
28.2.24 $b_{n}\left(0\right)=n^{2},$ $n=1,2,3,\dots$.
2: 32.1 Special Notation
 $m,n$ integers. …
3: 24.6 Explicit Formulas
24.6.2 $B_{n}=\frac{1}{n+1}\sum_{k=1}^{n}\sum_{j=1}^{k}(-1)^{j}j^{n}{\genfrac{(}{)}{0.% 0pt}{}{n+1}{k-j}}\Bigg{/}{\genfrac{(}{)}{0.0pt}{}{n}{k}},$
24.6.3 $B_{2n}=\sum_{k=1}^{n}\frac{(k-1)!k!}{(2k+1)!}\*\sum_{j=1}^{k}(-1)^{j-1}{2k% \choose k+j}j^{2n}.$
4: 27.19 Methods of Computation: Factorization
§27.19 Methods of Computation: Factorization
Techniques for factorization of integers fall into three general classes: Deterministic algorithms, Type I probabilistic algorithms whose expected running time depends on the size of the smallest prime factor, and Type II probabilistic algorithms whose expected running time depends on the size of the number to be factored. … Type II probabilistic algorithms for factoring $n$ rely on finding a pseudo-random pair of integers $(x,y)$ that satisfy $x^{2}\equiv y^{2}\pmod{n}$. …As of January 2009 the snfs holds the record for the largest integer that has been factored by a Type II probabilistic algorithm, a 307-digit composite integer. …The largest composite numbers that have been factored by other Type II probabilistic algorithms are a 63-digit integer by cfrac, a 135-digit integer by mpqs, and a 182-digit integer by gnfs. …
5: 27.6 Divisor Sums
27.6.1 $\sum_{d\mathbin{|}n}\lambda\left(d\right)=\begin{cases}1,&n\mbox{ is a square}% ,\\ 0,&\mbox{otherwise}.\end{cases}$
27.6.2 $\sum_{d\mathbin{|}n}\mu\left(d\right)f(d)=\prod_{p\mathbin{|}n}(1-f(p)),$ $n>1$.
27.6.7 $\sum_{d\mathbin{|}n}\mu\left(d\right)\left(\frac{n}{d}\right)^{k}=J_{k}\left(n% \right),$
7: 14.27 Zeros
• (a)

$\mu<0$, $\mu\notin\mathbb{Z}$, $\nu\in\mathbb{Z}$, and $\sin\left((\mu-\nu)\pi\right)$ and $\sin\left(\mu\pi\right)$ have opposite signs.

• (b)

$\mu,\nu\in\mathbb{Z}$, $\mu+\nu<0$, and $\nu$ is odd.

9: 26.12 Plane Partitions
A plane partition, $\pi$, of a positive integer $n$, is a partition of $n$ in which the parts have been arranged in a 2-dimensional array that is weakly decreasing (nonincreasing) across rows and down columns. …
26.12.3 $B(r,s,t)=\{(h,j,k)\>|\>1\leq h\leq r,1\leq j\leq s,1\leq k\leq t\}.$
10: 24.10 Arithmetic Properties
where $n\geq 2$, and $\ell(\geq 1)$ is an arbitrary integer such that $(p-1)p^{\ell}\mathbin{|}2n$. … valid when $m\equiv n\pmod{(p-1)p^{\ell}}$ and $n\not\equiv 0\pmod{p-1}$, where $\ell(\geq 0)$ is a fixed integer. …valid for fixed integers $\ell(\geq 0)$, and for all $n(\geq 0)$ and $w(\geq 0)$ such that $2^{\ell}\mathbin{|}w$. … where $M(\geq 2)$ and $b$ are integers, with $b$ relatively prime to $M$. … valid for fixed integers $\ell(\geq 1)$, and for all $n(\geq 1)$ such that $2n\not\equiv 0$ $\pmod{p-1}$ and $p^{\ell}\mathbin{|}2n$. …