Question

if n is an odd integer then show that
$n {}^{2} \: - \: 1$

is divisible by 8

Answer 1

$Let \: the \: value \: of \: n \: be \: 3 \\ \\ Then \\ \: \: \: \: \: \: \: \: \: \: \: \: \: ({n}^{2} - 1) \div 8 \\ ( {3}^{2} - 1 ) \div 8\\ (9 - 1) \div 8 \\ 8 \div 8 = 1$