I'm not sure what you're asking with the part in blue, but I can address the statement that (n-1)n(n+1) is divisible by 24loadedx wrote:Need help with this concept:
When n is odd
n^3-n or (n-1)n(n+1) is divisible by 24
Let's take n equal to 1
1^3-1 = 0
1 is odd
0 is even
2 is even
Thank you for your help!
First notice that n-1, n, and n+1 represent 3 consecutive integers (for any integer n)
Next, there's a nice rule that says "among any n integers, one the numbers will be divisible by n"
So, one of the three integers (n-1, n, and n+1) will be divisible by 3
Next notice that, if n is odd, then n-1 and n+1 are even (i.e., divisible by 2)
Also notice that every second even number is divisible by 4.
So, of the 3 consecutive integers, we know that one is divisible by 2, one is divisible by 3, and one is divisible by 4
This means that their product must be divisible by (2)(3)(4) or 24
Cheers,
Brent
