prove that the difference of squares of any two odd numbers is divisible by 4. (first list at least 3 examples to support this statement.)

Answer 1

3^2 - 1^2 = 8 = 4*2
5^2 - 3^2 = 25 - 9 = 4*4
7^2 - 3^2 = 40 = 4*10

For any integer n, 2n+1 is odd.
Consider a pair of integers m and n.
The difference of the squares of odd integers can be written
(2n+1)^2 - (2m+1)^2 = 4n^2 - 4m^2
- 4(n+m)

= 4(n^2 - m^2 + n - m)
which is clearly evenly divisible by 4.