Question 130501
a odd number is x=2n+1
then x*x=(2n+1)(2n+1)=4n^2 + 4n + 1

then x^2-1=4n^2 + 4n
          =4n(n+1)

the n will be a odd or a pair number

1)now if the n is a odd number then n=2m+1 will m>=0 then n+1=2m+2 ==> 
n+1= 2(m+1)

with this 
x^2-1=4n(n+1) 
     =4n(2(m+1)) = 8n(m+1) then divisible by 8

2) if the n is a pair number then n=2m
x^2-1=4n(n+1)=8m(n+1)
then divible by 8

cheers