New posts in Contest Math

Homogenization, what it is in inequalities and how to utilize it to its fullest.

Angles enclosed in parallel lines

Determine if the Diophantine equation $x^{2008}-y^{2008}=2^{2009}$ has any solutions.

If $H$ is a subgroup of infinite index and $G = H \cup H_1 \cup H_2 \cup \cdots \cup H_p$, show that $G = H_1 \cup H_2 \cup \cdots \cup H_p$.

When are eight integers entirely determined by their pairwise sums?

Find all the integer pairs $(x, y)$ which satisfy the equation $x^5-y^5=16xy$

Proving $6(x^3+y^3+z^3)^2 \leq (x^2+y^2+z^2)^3$, where $x+y+z=0$

An application of the Casey's theorem.

Fast way to solve $4 = \sqrt[3] {x+10}-\sqrt[3] {x-10}$

Find the $26^{th}$ digit of a $50$ digit number divisible by $13$.