1) Prove that there are infinitely many positive integers $n$ such that there exists a permutation of $1, 2, 3, . . . , n$ 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?