KCC's Quiz AQQ300 about Divisibility by 6

(n^5 -1) = n(n-1)(n+1)(n^2 + 1)

n-1, n, n+1 are three consecutive integers. Therefore, one of them must be divisible by 3 and at least one must be divisible by 2. We can conclude that the product of these two integers must be divisible by 6.

(n^5 -1) = n(n-1)(n+1)(n^2 + 1)

n-1, n, n+1 are three consecutive integers. Therefore, one of them must be divisible by 3 and at least one must be divisible by 2. We can conclude that the product of these two integers must be divisible by 6.

Bravo Ryeder , you get it! The key point is to have found that 3 consecutive numbers must have a multiple of 2 and a multiple of 3 in them!