Let $ABCD$ be a trapezoid of parallel bases $ BC$ and $AD$. If $\angle CAD = 2\angle CAB, BC = CD$ and $AC = AD$, determine all the possible values of the measure of the angle $\angle CAB$.

How many dominoes can be placed on a at least $3 \times 12$ board, such so that it is impossible to place a $1\times 3$, $3 \times 1$, or $ 2 \times 2$ tile on what remains of the board? Clarification: Each domino covers exactly two squares on the board. The chips cannot overlap.

Find all functions $f\colon \mathbb{R}\to\mathbb{R}$ such that \[f(x + y) + f(x + z) - f(x)f(y + z) \ge 1\]for all $x,y,z \in \mathbb{R}$

Let $a>2$, $n>1$ integers such that $a^n-2^n$ is a perfect square. Prove that $a$ is a even number.