Question

if n is the odd number then show that n square minus 1 is divisible by 8​

Answer 1

Answer: odd number is of form (2q+1) where q is a natural no.

So,n2-1=(2q+1)2-1

n2-1=4q2+4q+1-1

Cancelling 1 we get

n2-1=4q2+4q

Now checking,

Q=1,then

4q2+4q=4(1)2+4(1)

4+4=8,it is divisible by8

Q=2

4(2)2+4(2)=4(4)+8=16+8

24,it is divisible by8

Q=3

4(3)2+4(3)=4(9)+12=36+12

48,it is divisible by 8

Hence we can conclude that 4q2+4q is divisible by8 for natural no. Hence n2-1 is is divisible by 8 for any value of n including odd number.

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