证明：当 max {ai} −min {ai}=(r−l)×gcdl≤i<r{∣ai−ai+1∣}\max \ \{a_i\}\ -\min\ \{a_i\}=(r-l)\times\gcd \limits_{l\leq i< r}\{|a_i-a_{i+1}|\}max {ai} −min {ai}=(r−l)×l≤i<rgcd{∣ai−ai+1∣} 时，
al,al+1...,ar−1,ara_l,a_{l+1}...,a_{r-1},a_{r}al,al+1...,ar−1,ar 是等差数列。
