先看一看下面的两个命题:1.两个相邻偶数的乘积加上1是一个完全平方数.2.四个连续整数的乘积加上1是一个完全平方数.这是两个熟知的命题,证明都是基于代数式变形中的配方.注意到,一个完全平方数减去1可以通过平方差变为两个式子的乘积,上述两个命题都是对此问题经“逆向思考”后得到的.本文就这类完全平方数介绍一些性质和结论.例1设a、6为正整数,且nb+1是完 Let’s take a look at the following two propositions: 1. The product of two adjacent even numbers plus 1 is a complete square number. 2. The product of four consecutive integers plus 1 is a complete square number. These are two well-known Propositions, proofs are based on formulas in algebraic variants. Note that a complete square number minus 1 can be a product of two squares by squared difference. Both of these propositions are “reverse thinking” on this question. After that, this article introduces some properties and conclusions about this type of complete square number. Example 1 Let a, 6 be positive integers, and nb+1 is the end