已知n是正整数,求证(n^2+3n+1)^2-1是连续四个整数的乘积

问题描述:

已知n是正整数,求证(n^2+3n+1)^2-1是连续四个整数的乘积

证明:
(n^2+3n+1)^2-1
=(n^2+3n+2)(n^2+3n)
=(n+1)(n+2)n(n+3)
=n(n+1)(n+2)(n+3)