frac{a}{b}+\frac{b}{a} \notin \mathbb{Z}$
20593
Show that if $a \neq b$ and a and b are positive then $\frac{a}{b}+\frac{b}{a}$ is never an integer
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
119628
Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$
33240
$ \frac{1}{a^{2} + b^{2} + 1} + \frac{1}{b^{2}+c^{2}+1} + \frac{1}{c^{2} + a^{2} + 1} \ge 1 $, prove $ab + bc + ca \le 3$
93756
$1+\frac{1}{2} +\frac{1}{3} +...+\frac{1}{p-1} =\frac{a}{b}$
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$
113380
Prove that $\left | \frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a} \right | < \frac{1}{8}.$
101491
If $\frac{a}{|z_2-z_3|}=\frac{b}{|z_3-z_1|}=\frac{c}{|z_1-z_2|}$, then why is $\frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}=0$?
68389
Proving $ \frac{(a-b)^2}{8a}\leqslant\frac{a+b}{2} - \sqrt{ab} \leqslant\frac{(a-b)^2}{8b}$ when $ 0<b\le a$
154822
Properties of the composition law $a @ b= ab + b + a$ on the real numbers
133382
Proof that $a+b+\frac{1}{1+\sqrt{ab}}\geq\frac{5}{2}$
57670
Show that $|z_1 + z_2|^2 < (1+C)|z_1|^2 + \left(1 + \frac{1}{C}\right) |z_2|^2$
139111
Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
44928
Show $\sum_n \frac{z^{2^n}}{1-z^{2^{n+1}}} = \frac{z}{1-z}$
138559
How can I show that $\frac{1}{1+|z|^2}$ isn't analytic at $z=1$?
77777
If $0\le a,b,c\le 1$, then $\frac a{1+bc}+\frac b{1+ac}+\frac c{1+ab}\le 2$
154716
Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$