Is this an error in Guide 1? pg. 151 example

[bdetrent]

x^3 - x = p and x is odd, is p divisible by 24?

p = x(x - 1)(x + 1) -- the guide says "p is divisible by at least 4," because (x - 1) is even and (x + 1) is even cuz x is odd.

However, what if X is 1? Then p = 0

Pls tell me if I'm missing something

[gayathri248]

0 divided by anything is still 0. Its still considered divisible.

[tim]

Yes, in other words 0 is divisible by 4, and it is in fact divisible by any nonzero integer you can name. Remember, to be divisible by 4, a number n must have the property that n/4 is an integer. Since 0/4 is an integer (0), 0 is divisible by 4. You can of course use this method to verify that 0 is divisible by any integer for which divisibility is defined..