Here are Questions 1-3.
Question 1.
$ Let $n$ be a positive integer and let $a_1,a_2,a_3,\ldots,a_k$ $\left( k\ge 2\right)$ be distinct integers in the set $\left\{ 1,2,\ldots,n\right\}$ such that $n$ divides $a_i(a_{i + 1} - 1)$ for $i = 1,2,\ldots,k - 1$. Prove that $n$ does not divide...