Question

Show that n²-1 is divisible by 8, if n is odd positive integer.

Answer 1

Heya!!

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To show : n^2 - 1 is divisible by 8, if n is odd positive number.

Since we can write odd no as 4q+1 where q is any natural no.

Hence n=(4q+1)

A/Q

= n^2 - 1 = (4q+1)^2 - 1

= (4q)^2 + 2(4q)(1) + (1)^2 - 1

= 16q^2 + 8q +1 - 1

= 16q^2 + 8q

Take 8 as common,

= 8(2q^2 + q)

= 8m (where m= 2q^2 + q)

Hence 8 is a factor of n^2 - 1 if n is odd positive integer.

Hope it helps u :)