How to prove $(-1)\cdot x = -x$ in a field?
111515
Proving that $-a=(-1)\cdot a$
121441
$1\cdot3\cdot5 \cdots (p - 2) = (-1)^{m+k+1} \pmod p$, and $2\cdot4\cdot6\cdots(p - 1) = ( -1)^{m +k} \pmod p$.
140898
Is $v=\ (r_i)^{-1}\cdot z $, a uniformly random value of a field?
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
111505
Proof $\binom{p-1}{k}\equiv (-1)^k \mod{p}$
63410
Proof on showing if F(x,y,z)=0 then product of partial derivatives (evaluated at an assigned coordinate) is -1
6128
If $a \cdot a = 1$ then $a = 1$ or $a = -1$
39514
how do I prove that $1 > 0$ in an ordered field?
6539
Prove $\sum_{i=1}^n i! \cdot i = (n+1)! - 1$?
4401
Constructive proof that algebraic numbers form a field
130854
Constructing example showing $\mathbb{E}(X^{-1})=(\mathbb{E}(X))^{-1}$
84562
Proof using only field axioms
140474
Why is Ext$(-;k) =0$ when $k$ is a field
62254
Show $F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n$ for all $n \in \mathbb{N}$
37723
Proof that $-(-x) = x$ using just the field axioms
58633
Proof of the formula $1+x+x^2+x^3+ \cdots +x^n =\frac{x^{n+1}-1}{x-1}$
107071
Prove $\sum_{k= 0}^{n} k \binom{n}{k} = n \cdot 2^{n - 1}$ using the binomial theorem