If n 4k 3 does 8 divide n2 1 Give a reason for your answe

If n = 4k + 3, does 8 divide n^2 - 1? Give a reason for your answer.

Solution

Solution:

Yes 8 divides n² -1

Proof:

Let n=4k+3 Then

n²-1=(4k+3 )² -1

    =16k²+24k+9-1

   =16k²+24k+8

=8(2k² +3k+1)

Therefore,8 divides n²-1

Hence proved.