Stairs are built by laying bricks as shown in the figure. If you have $2004$ bricks to build a staircase: a) How many steps (= escalones) will the ladder have? b) How many bricks will there be left over?

Determine for what values of $x$ the expressions $2x + 2$,$x + 4$, $x + 2$ can represent the sidelengths of a right triangle.

In an equilateral triangle $ABC$, whose side is $4$, the line perpendicular to $AB$ is drawn through the point $ A$, the line perpendicular to $BC$ through point $ B$ and the line perpendicular to $CA$ through point $C$. These three lines determine another triangle. Calculate the perimeter of this triangle

In a square $ABCD$, $E$ is the midpoint of $BC$ and $F$ is the midpoint of $CD$. Prove that $AF$ and $AE$ divide the diagonal $BD$ in three equal segments.

We have an integer $A$ such that $A^2$ is a four digit number, with $5$ in the ten's place . Find all possible values of $A$.