Legendre Symbol: Prove that if $(a,p)=1$ and $p$ is an odd prime, then $\sum^p_{n=1}\left(\frac{an+b}{p}\right)=0$.
48482
Legendre symbol: Showing that $\sum_{m=0}^{p-1} \left(\frac{am+b}{p}\right)=0$
50781
$(n+1)$th prime $p_{n+1}$ less than or equal to $p_1p_2\dots p_n+1$
20980
Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
46410
sum of the product of consecutive legendre symbols is -1
145019
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
93756
$1+\frac{1}{2} +\frac{1}{3} +...+\frac{1}{p-1} =\frac{a}{b}$
18914
How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
136476
Find the values of $p$ such that $\left( \frac{7}{p} \right )= 1$ (Legendre Symbol)
58526
Proving Legendre's Formula
49217
How do I show that $a^p + b^p > (a + b)^p$ for $a,b>0$ and $0<p<1$?
118305
Let $p$ be an odd prime. $p$ and $(1-\zeta_p)^{p-1}$ are associates in $\mathbb{Z}[\zeta_p]$.
14480
Proving $(P(AB))^2+(P(AB^c))^2+(P(A^cB))^2+(P(A^cB^c))^2\ge\frac{1}{4}$ for any events $A$ and $B$
16143
How can I prove that $\sum_{n=1}^\infty \frac{1}{n(n+1)} = 1$?
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.