Spring 2017, problem 35
Let $m_1,m_2,m_3,\dots,m_n$ be a rearrangement of the numbers $ 1,2,\dots,n$. If $ n$ is odd, show that the product $$ \left(m_1-1\right)\left(m_2-2\right)\cdots \left(m_n-n\right)$$ is an even integer.
Let $m_1,m_2,m_3,\dots,m_n$ be a rearrangement of the numbers $ 1,2,\dots,n$. If $ n$ is odd, show that the product $$ \left(m_1-1\right)\left(m_2-2\right)\cdots \left(m_n-n\right)$$ is an even integer.