Prove that $\frac{x+y}{1+xy}$ is an Abelian Group
17510
Proving a set is an abelian group.
46260
Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
33233
Need to prove that $(S,\cdot)$ defined by the binary operation $a\cdot b = a+b+ab$ is an abelian group on $S = \Bbb R \setminus \{-1\}$.
102391
Abel summability under the hypothesis $a_n \ge 0$
83557
$\frac{x^2}{y+z}+\frac{y^2}{x+z}+\frac{z^2}{x+y} \ge \frac{1}{2}(x+y+z)$
76317
Let $C$ be the commutator subgroup of $G$. Prove that $G/C$ is abelian
103851
Show that $\frac{xy}{z} + \frac{xz}{y} + \frac{yz}{x} \geq x+y+z $ by considering homogeneity
98542
Prove that $H$ is a subgroup of an abelian group $G$
136782
Prove that $x * y = \frac{x+y}{1+xy}$ is a stable part of $G=(-1, 1)$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
49882
Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective
82742
Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
25825
Proof that $\gcd(ax+by,cx+dy)=\gcd(x,y)$ if $ad-bc= \pm 1$
73571
Proof of Cauchy's Theorem for abelian groups
141643
Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
81671
Proof of identity $\sqrt {xy} = \sqrt x \sqrt y$ for $x,y \in \mathbb R^+$
43783
Abelian group (Commutative group)