n(n+1)(n+2)(n+3)+1

问题描述:

n(n+1)(n+2)(n+3)+1
为什么n×(n+1)×(n+2)×(n+3)+1=(n^2+3n+1)^2

(n^2+3n+1)^2
说明n(n+3)=n^2+3n
(n+1)(n+2)=n^2+3n+2
所以n(n+1)(n+2)(n+3)=(n^2+3n)^2+2(n^2+3n)最后再加1又变成一个完全平方了