\[\boxed{\text{682}\text{\ (682)}\text{.}\text{\ }\text{Еуроки\ -\ ДЗ\ без\ мороки}}\]
\[x_{m} = x_{1} + d(m - 1)\]
\[x_{n} = x_{1} + d(n - 1)\]
\[\Longrightarrow x_{m} - x_{n} = x_{1} + dm - d - x_{1} - dn + d = dm - dn = d \cdot (m - n)\]
\[\Longrightarrow x_{m} - x_{n} = d \cdot (m - n) \Longrightarrow d = \frac{x_{m} - x_{n}}{m - n} \Longrightarrow ч.т.д.\]