Question

n^2 -1 is divisible by 8,if n is

Answer 1

Answer: an odd no.

Step-by-step explanation: if n is even then n can be in the form 2q

then n^2 will be even (4q) then n^2 -1 will be odd

If n is odd then n can be written in the form 2q +1

n^2 will be (2q+1)^2

4q^2+4q+1

Then n^2 -1 wil be in the form 4q^2+4q

4(q^2+q)

Even +even is even

Odd +odd is also even so in any case q^2 +q will be even

Therefore n^2-1 will be 4(2c)

i.e. 8 c which is divisible by 8

Hence n is odd

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