N is a positive odd integer then n^2-1 is divisible by 8?

GRE Quant Problem Solving
1

I understand that you can write n^2 - 1 as (n-1)(n+1) and if you choose odd numbers from 3 onward the equation is divisible by 8.

However, if we input n = 1, since it is an odd positive integer, the equation fails since the answer is not an integer. Am I correct? If I am correct then how does the proof work here? [1]

[1] https://math.stackexchange.com/questions/199185/proof-problem-show-that-n2-1-is-divisible-by-8-if-n-is-an-odd-positive

2

Hello @javaid.salman,

If you choose n = 1, then (n+1)(n-1) becomes (1+1)(1-1) = 0.
And, zero is valid because it is an integer, and it is indeed divisible by 8. (0/8 = 0)
This case is also valid. :smiley: