New posts in Contest Math

Combinatorics on divisors

Prove that connected graph $G$ with $\delta (G)\geq 3$ contains a cycle $C$ such that $G-E(C)$ is still connected.

Construction of symmedians but different.

$ \sum_{i=1}^{10} x_i =5 $, and $ \sum_{i=1}^{10} x_i^2 =6.1 $ ; Find the largest value of these ten numbers

Prove that $\frac{a^{2}+1}{b}+\frac{b^{2}+1}{a} \geq 4$

Hard problems solving tricks

Minimum of $\left|1-\left(ab+bc+ca\right)\right|+\left|1-abc\right|$

Proving $abcd+3\geq a+b+c+d$

A polynomial divisible by primes of special form

Prove the roots of $z^7+7z^4+4z+1=0$ lie inside a circle of radius $2$.