设这四个连续的整数为n,n+1,n+2,n+3,则有
n(n+1)(n+2)(n+3)+1=(n^2+3n)(n^2+3n+2)+1=(n^2+3n)^2+2(n^2+3n)^2+1
=(n^2+3n+1)^2
注:^2是平方