證明：可設(shè)這4個(gè)連續(xù)整數(shù)依次為n、n+1、n+2、n+3,則有
n(n+1)(n+2)(n+3)+1
=n(n+3)(n+1)(n+2)+1
=(n^2+3n)(n^2+3n+2)+1
=(n^2+3n)^2+2(n^2+3n)+1
=(n^2+3n+1)^2
所以說(shuō)4個(gè)連續(xù)整數(shù)的積與1的和是一個(gè)完全平方數(shù).