Proving $p^2q+q^2r+r^2p+pq^2+qr^2+rp^2\geq 6pqr$
31544
How to prove that this polynomial is larger than another for positive reals?
82016
Given $p^2+q^2+r^2+1=s+\sqrt{p+q+r-s}$, solve for $s$
112969
Show that $ab + bc + ac \ge a\sqrt{bc} + b\sqrt{ac} + c\sqrt{ab}$
147307
How to evaluate $\sum_{\gcd (p,q)=1} \frac{1}{p^2q^2}$?
34768
Proving $(p \oplus q) \oplus r=p \oplus (q \oplus r)$
132098
Prove $(a^2+b^2)(c^2+d^2)\ge (ac+bd)^2$ for all $a,b,c,d\in\mathbb{R}$.
44403
Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$
91871
Proving quadratic inequalities?
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 $B$
121177
Prove that $\frac{(2a+b+c)^2}{2a^2+(b+c)^2}+\frac{(2b+c+a)^2}{2b^2+(c+a)^2}+\frac{(2c+a+b)^2}{2c^2+(a+b)^2} \le 8$
2019
Prove $\sqrt{a} + \sqrt{b} + \sqrt{c} \ge ab + bc + ca$
148744
Prove that $(\frac{bc+ac+ab}{a+b+c})^{a+b+c} \ge \sqrt{(bc)^a(ac)^b(ab)^c}$
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
125702
There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$
23638
$a^2b^2+a^2c^2+b^2c^2\leq 3$
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
85449
Show a,b,c congruences when $a^2+b^2=c^2$