Question

观察下列各式:1×2×3×4 1=25

Answer 1

设这四个数为n,(n+1),(n+2),(n+3)

n(n+1)(n+2)(n+3)+1

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

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

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

∴这个数为完全平方数