Question

If q^2-1 is divisible by 8 if q is _____

Answer 1

if q is odd

Explanation:

Hello,

Either q is odd or is even.

Case 1 - we can find k integer so that q = 2k

Then, in the case

`q^2-1=4k^2-1`

This is not divisible by 8, for instance, q = 6

`q^2-1=36-1=35=7*5`

Case 2 - we can find k integer so that q = 2k+1

`q^2-1=(2k+1)^2-1=4k^2+4k+1-1=4k(k+1)`

k(k+1) is divisible by 2 so the initial number is divisible by 8

Conclusion, the answer is q is odd.

Thanks