Question

Q.6- Show that n^2-1 (n square minus one) is divisible by 8, if 'n' is an odd positive integer.

Answer 1

Answer:

Step-by-step explanation:

I think you mean n²-1

any positive integer is equal to bq+r where 0≤r (lessthan) b (euclids division lemma)

any odd positive integer is equal to 4q+1 or 4q+3

substitute the value in it (n=4q+1 or 4q+3)

n²-1

=(4q+1)²-1         or    (4q+3)²-1

=16q²+8q+1-1   or    16q²+24q+9-1

=8q(2q+1)        or     8q(2q+3)

which both have 8 as a factor, hence proved.