Question

show that n^2-1 is divisible by 8 if n is odd positive integer {n square-1}

Answer 1

An odd integer n is either a 4k+1 or a 4k+3. (4k+1)2 – 1 = 16k2+ 8k + 1 - 1 =8(2k2 +k), which is a multiple of 8.