Question

证明：四个连续整数的积加上1是完全平方数

Answer 1

设四个连续整数为n,n+1,n+2,n+3

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)[(n^2+3n)+2]+1

=(n^2+3n)^2+2*(n^2+3n)+1

=(n^2+3n+1)^2

是一个完全平方数