Question 27
Let $m$, $n$ and $k$ be positive integers and let $p_1, p_2, \dots, p_n$ be the integers $1, 2, \dots, n$ given in some order. If
$$
k \mid (m + p_i - i),
$$
holds for all $i \in \{1, 2, \dots, n\}$, prove that one of the numbers $m$ and $n$ is divisible by $k$.
$$
k \mid (m + p_i - i),
$$
holds for all $i \in \{1, 2, \dots, n\}$, prove that one of the numbers $m$ and $n$ is divisible by $k$.