Use induction to prove that n21 is a multiple of 8 whenever

Use induction to prove that n^2-1 is a multiple of 8 whenever n is a positive odd integer.

Solution

N²-1=(N-1)(N+1)

GIVEN N IS ODD

=>N²-1=(2K+1-1)(2K+1+1)=2K(2K+2)=4K(K+1)

IF K IS ODD THEN K+1 IS EVEN OR VICE VERSA

=>K(K+1)=2.P

THER FORE N²-1=4.2P=8P

n^2-1 is a multiple of 8