## n2(n2−1)(n2−4)n^2(n^2-1)(n^2-4) is always divisible by 360 (n>2,n∈N)(n>2,n\in \mathbb{N})

How does one prove that n2(n2−1)(n2−4) is always divisible by 360? (n>2,n∈N) I explain my own way: You can factorize it and get n2(n−1)(n+1)(n−2)(n+2). Then change the condition (n>2,n∈N) into (n>0,n∈N) that is actually equal to (n∈N). Now the statement changes into : n(n+1)(n+2)2(n+3)(n+4) Then I factorized 360 and got 32⋅23⋅5. I don’t know how … Read more