Find the biggest value of $|a-b|+|b-c|+|c-a|$ when $a^2+b^2+c^2=1$
45439
Given reals $a_1, a_2, \cdots, a_{n - 1}, a_n$ such that $\sum_{i = 1}^na_1^2 = 1$. Calculate the maximum value of $\sum_{cyc}|a_1 - a_2|$.
85449
Show a,b,c congruences when $a^2+b^2=c^2$
24499
Finding $(a, b, c)$ with $ab-c$, $bc-a$, and $ca-b$ being powers of $2$
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
73716
Let $x,y,z>0$ and $x+y+z=1$, then find the least value of ${{x}\over {2-x}}+{{y}\over {2-y}}+{{z}\over {2-z}}$
17751
Find the greatest value of $\arg z$ achieved on a circle in $\mathbb{C}$
83124
Maximize :: $A = B \times C$
26287
Find $\frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ if $a+b+c=0$
144512
Find the greatest value of $a^2\cdot b^3$ where $a+b=10$
16382
Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$
113168
If $a > b$, is $a^2 > b^2$?
56796
Maximum of $x^3+y^3+z^3$ with $x+y+z=3$
20478
Mathematical expression for $n$ largest values in a set
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
87907
How to find the maximum and minimum value of $\left|(z_1-z_2)^2 + (z_2-z_3)^2 + (z_3-z_1)^2\right|$ (where $|z_1|=|z_2|=|z_3|=1$)?
52546
How can I find the possible values that $\gcd(a+b,a^2+b^2)$ can take, if $\gcd(a,b)=1$
82317
Find the minimum value of $A=\frac{2-a^3}{a}+\frac{2-b^3}{b}+\frac{2-c^3}{c}$