Phan Thanh Tinh Coordinator 11/08/2017 at 15:38
Denote A = n2(n4 - 1) = n2(n2 - 1)(n2 + 1) is the product of 3 consecutive integers,so \(A⋮3\).We have :
If n is even,then \(n^2⋮4\) and \(A⋮4\)
If n is odd,then n - 1 and n + 1 is even. So,\(A⋮4\)
\(\left(n-2\right)\left(n-1\right)n^2\left(n+1\right)\left(n+2\right)\)include the product of 5 consecutive integers,so it's divisible by 5.Moreover, \(5n^2\left(n^2-1\right)⋮5\)
Since A is divisible by 3,4,5 and 3,4,5 are relatively prime numbers, \(A⋮3.4.5=60\)Kaya Renger selected this answer.
Please help Kaya Renger to solve this problem!