Show that: n² - 1 is divisible by 8 if n is an odd positive integer.

Odd positive integers are odd numbers greater than zero. Integers are denoted by 'z'.

Answer: n² - 1 is divisible by 8 for n is an odd positive integer.

Let's see how we can prove this.

Explanation: 

Let n = 4z +1 where z is an positive integer. 

On substituting the value of z in n² - 1, we get

⇒ ( 4 z + 1)²  - 1 = 0

⇒ 16z² + 1 + 8 z - 1 = 0

⇒ 16z²  + 8 z = 0

⇒ 8z ( 2 z + 1) = 0

Since (2z + 1) is an odd number and a multiple of 8, it is also divisible by 8.

Thus, n² - 1 is divisible by 8 if n is an odd positive integer.