證明:設(shè)這個(gè)連續(xù)整數(shù)為:n,n+1,n+2,n+3,
這四個(gè)連續(xù)的整數(shù)的積與1的和
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).