If n is a positive iteger and r is th remainder when n² - 1 is divided by 8, what is the value of r?

(1) n is odd.
(2) n is not divisible by 8.

When trying to use statement 1, as far s I see, all odd numbers have a remainder of 0. For example:
3² - 1 = 8, Quotient: 1, Remainder: 0
5² - 1 = 24, Quotient: 3, Remainder: 0
7² - 1 = 48, Quotient: 6, Remainder: 0
9² - 1 = 80, Quotient: 10, Remainder: 0
11² - 1 = 120, Quotient: 15, Remainder: 0
13² - 1 = 168, Quotient: 21, Remainder: 0
15² - 1 = 224, Quotient: 28, Remainder: 0

Any thoughts on this?