Prove by contradiction: For any integer n, n^2 - 2 is not divisible by 4 Solution let us suppose n2 - 2 is divisible by 4 n2 - 2 = 4k n2 = 4k + 2 n2 = 2(2k+1) n2 = even ==> n is even let n = 2m ; n2 = 2(2k+1) ==> 4m2 = 2(2k+1) ==> 2m2 = (2k+1) where m and k are integers ==> even = odd Therefore , our assumption that n2 - 2 is divisible by 4 is wrong Hence, For any integer n, n^2 - 2 is not divisible by 4.