Question

If
$n$
is an odd odd integer then show that
${n}^{2} - 1$
is divisible by 8.​

Answer 1

Answer:

hey mate

here is your answer

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.

(4k+3)2 – 1 = 16k2+ 24k + 9 - 1 =8(2k2 +3k + 1), which is a multiple of 8.

hope it will help uhh