A problem with the Legendre/Jacobi symbols: $\sum_{n=1}^{p}\left(\frac{an+b}{p}\right)=0$
48482
Legendre symbol: Showing that $\sum_{m=0}^{p-1} \left(\frac{am+b}{p}\right)=0$
148970
How to calculate such sums of Legendre symbols?
2722
Exploring $ \sum_{n=0}^\infty \frac{n^p}{n!} = B_pe$, particularly $p = 2$.
78473
Showing $ \sum_{n=0}^{\infty} \frac{1}{(3n+1)(3n+2)}=\frac{\pi}{3\sqrt{3}}$
129801
Finding a closed form for $\sum^{n}_{k=1} \frac{k}{(k+1)!} $
107060
Confusion in proof for writing Poincares series in terms of Kloosterman sum
83457
Given the pdf $f(y\mid\theta) = \theta y^{\theta - 1}1_{0<y<1}$, show $E\left(\frac{1}{2\theta\sum_{i = 1}^n W_i}\right) = \frac{1}{2(n-1)}$
27494
$P_n(x):=1+ \sum_{m=1}^n\dfrac{x^m}{m!}$ has no real root for even $n$ and exactly one real root for odd $n$
81124
Infinite product problem: $\sum p_n0$
121617
Closed form of $\sum_{n=0}^{\infty} \frac{\cos(\alpha \, n)}{n!}$
143428
How to sum $\sum_{x=0}^{N-1} \cos{\left( \frac{2\pi x}{N} \right)}^{2}$?
45171
How prove this $(p-1)!\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\right)\equiv 0\pmod{p^2}$
109599
A finite sum involving the binomial coefficients and the harmonic numbers
82621
Show $P\{\xi_1+\dots+\xi_n=1\}=(\sum_{i=1}^n \lambda_i)\Delta + O(\Delta^2)$ (Shiryaev's Probability page 44)
32637
What is the sum of this series: $\displaystyle\sum_{n=0}^{\infty} \dfrac{a^n}{(3n)!}$
36701
$\displaystyle\int_{0}^{2\pi}\frac{1}{a+ \cos\theta}\,d\theta$
29693
Would someone please explain this argument? (Legendre formula)