If a is an odd integer, then 24|a(a^2-1)

[@matheusjahnke8643]

a(a²-1)=(a-1)a(a+1)... a product of 3 consecutive numbers; one of them is guaranteed to be a multiple of 3 now consider that a is odd... which means both a-1 and a+1 are even; Furthermore, since a=4n+1 or a=4n-1, either a-1 or a+1 are a multiple of 4; So one is a multiple of 4, and the other is a multiple of 2... hence the product will be at least a multiple of 8; Since the a(a²-1) is a multiple of 3 and of 8.... it must be a multiple of the least common multiple between the 3 and 8, which is 24.

[@snellbrosmath]

That's sly my guy 😉

[@matthewward1705]

Ooo I love this one!