定理 1　差为定值的两自然数之不同积 ,可排成二阶等差数列 ,二阶差为 2 .证明 :设定值为t,则数列 {an},an=n(n +t) ,于是an + 2 -2an+ 1+an=(n +2 ) 2 -2 (n +1 ) 2 +n2 +(n +2 )t-2 (n +1 )t+nt=2 .定理 2　商为定值t(t∈N)的两自然数的不同积 ,可排成二阶等差数列 ,二阶差为 Theorem 1 The differential product of the two natural numbers whose difference is a fixed value can be arranged as a second-order arithmetic series with a second-order difference of 2. Proof: The set value is t, then the series {an}, an=n(n+t) , so an + 2 -2an+ 1+an=(n +2) 2 -2 (n +1) 2 +n2 +(n +2)t-2 (n +1)t+nt=2. Theorem 2 The different product of the two natural numbers t(t∈N) can be arranged as a second-order arithmetic series, and the second-order difference is