Question

show that n²-1 is divisible by 8, if n is odd positive integer ​

Answer 1

Step-by-step explanation:

Let take n be any positive integer and just put that in the given equation

Answer 2

Answer:

n may be in the form of 4m+1 or 4m+3

case 1 when n=4m+1 :

n^2-1=(4m+1)^2-1

=16m^2-8m+1-1

=16m^2+8m

=8(2m^2+m)

it is divided by 8

case 2 when n=4m+3

n^2-1 = (4m+3)^2-1

=16m^2+24m-9-1

=16m^2+24+8

=8(2m^2+3m+1)

it is also divided by 8

i.e. n^2-1 is divided by 8