x3-x=p,x=odd p divisible by 24

[shivaankarkumara]

in number property guide 4th edition page 151

it says
p=(x-1)(x)(x+1)
if x is odd (x-1)and (x+1) even-agreed
it further says p is divisible by atleast 4
how so
q)if x is odd x can be 1
x-1=0(even)
x+1=2(even)
this is not divisile by 4
and the odd no x not divisible by 3

please explain

[jnelson0612]

in number property guide 4th edition page 151

it says
p=(x-1)(x)(x+1)
if x is odd (x-1)and (x+1) even-agreed
it further says p is divisible by atleast 4
how so

If x is odd, I have that p is even * odd * even. Each of those evens is divisible by 2, so each even is contributing at least one 2 to the final product. So I have even (2 * other factors) * odd * even (2 *other factors). 2*2 = 4, so p must be divisible by 4.

q)if x is odd x can be 1
x-1=0(even)
x+1=2(even)
this is not divisible by 4
and the odd no x not divisible by 3

please explain

Actually, 0 * odd * 2 will equal 0, which is divisible by 4, because zero is divisible by all integers.