Prove that for any integer the number $2n^3+3n^2+7n$ is divisible by $6$.

Solve $|x-1|-2|x+5|>3+x$.

A student read the book with $480$ pages two times. If he in the second time for every day read $16$ pages more than in the first time and he finished it $5$ days earlier than in the first time. For how many days did he read the book in the first time?

The number $2015$ has been written in the table. Two friends play this game: In the table they write the difference of the number in the table and one of its factors. The game is lost by the one who reaches $0$. Which of the two can secure victory?

A square $ABCD$ with sude length 1 is given and a circle with diameter $AD$. Find the radius of the circumcircle of this figure.

Let $a$ and $b$ be the solutions to $x^2-x+q=0$, find $a^3+b^3+3(a^3b+ab^3)+6(a^3b^2+a^2b^3)$.