Question

$n { }^{2} - 1 \: is \: divisible \: by \: 8 \: if \: n \: is$

Answer 1

Answer :-

n is odd

Explanation

As we know that

odd - 1 = even

and

even - 1 = odd

And

odd² = odd

Even² = Even

Now let us consider a odd integer

2m +1

Where m is any positive integer.

Now squaring of the integer

= (2m +1)²

= (2m)² + 2(2m)(1) + (1)²

= 4m² + 4m + 1

Now n² - 1

= 4m² + 4m + 1 - 1

= 4m² + 4m

= 4m( m + 1)

as m is any positive integer

Hence 4m(m+1) is divisible by 8