Solve in the set of real numbers, the system: $$x(3y^2+1)=y(y^2+3)$$$$y(3z^2+1)=z(z^2+3)$$$$z(3x^2+1)=x(x^2+3)$$

Find all positive integer solutions of the equation $n^5+n^4=7^{m}-1$

We have an acute triangle $ABC$. Consider the square $A_1A_2A_3A_4$ which has one vertex in $AB$, one vertex in $AC$ and two vertices ($A_1$ and $A_2$) in $BC$ and let $x_A=\angle A_1AA_2$. Analogously we define $x_B$ and $x_C$. Prove that $x_A+x_B+x_C=90$

Each of the squares on a $15$×$15$ board has a zero. At every step you choose a row or a column, we delete all the numbers from it and then we write the numbers from $1$ to $15$ in the empty cells, in an arbitrary order. find the sum possible maximum of the numbers on the board that can be achieved after a number finite number of steps.