Question 140
1) Prove that there are infinitely many positive integers $n$ such that there exists a permutation of $1,2,3, \ldots, n$ with the property that the difference between any two adjacent numbers is equal to either $2015$ or $2016$.
2) Let $k$ be a positive integer. Is the statement in 1) still true if we replace the numbers $2015$ and $2016$ by $k$ and $k+2016$, respectively?
2) Let $k$ be a positive integer. Is the statement in 1) still true if we replace the numbers $2015$ and $2016$ by $k$ and $k+2016$, respectively?