For convex cyclic hexagon $ABCDEF$, show $AC\cdot BD \cdot CE \cdot DF \cdot EA\cdot FB \geq 27\cdot AB\cdot BC\cdot CD \cdot DE\cdot EF\cdot FA$
96590
Convex cyclic hexagon $ABCDEF$. Prove $AC \cdot BD \cdot CE \cdot DF \cdot AE \cdot BF \geq 27 AB \cdot BC \cdot CD \cdot DE \cdot EF \cdot FA$
21788
Proving that if $ad-bc = \pm 1$, then $\gcd(x,y) = \gcd(ax +by, cx + dy)$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
73799
In a convex Quadrilateral ABCD, $\measuredangle ABC = \measuredangle BCD = 120^{\circ}$.Prove that: $ AC + BD \ge AB + BC + CD$
57096
Show that $\max{\{|a|+|b|,|c|+|d|\}} \leq \max{\{|a|,|c|\}}+\max{\{|b|,|d|\}}.$
6335
Proving that the set enclosed by an ellipse is convex
93599
General Proof for the triangle inequality
136644
Cyclic Quadrilateral Problems
156966
Prove that if $b = dk$ where $gcd(m, a) = d$, there are $d$ solutions to $ax \equiv b \mod m$
107716
Show that $G$ is cyclic
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
116382
Showing convexity of a function with the restriction over an arbitrary line
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
116851
Show that f(x) is convex
127032
Maximum of $\cos \alpha_{1}\cdot \cos \alpha_{2}\cdot \cos \alpha_{3}....\cos \alpha_{n}.$
40403
Show that the function is convex
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?