Question

if n is an odd number then prove that n² - 1 is divisible by 8

Answer 1

Question:-

if n is an odd number then prove that n² - 1 is divisible by 8

${\red{\underline{\underline{\bold{Answer:-}}}}}$

Any odd positive integer n can be written in form of 4q + 1 or 4q + 3.

If n = 4q + 1, when n2 - 1 = (4q + 1)2 - 1 = 16q2 + 8q + 1 - 1 = 8q(2q + 1) which is divisible by 8.

If n = 4q + 3, when n2 - 1 = (4q + 3)2 - 1 = 16q2 + 24q + 9 - 1 = 8(2q2 + 3q + 1) which is divisible by 8.

So, it is clear that n2 - 1 is divisible by 8, if n is an odd positive integer.

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Answer 2

Answer:

Let n be 5

we have to prove that n²- 1 is divisible by 8

So, n²-1/8 = 5²-1/8

25-1/8

24/8

= 3 is the answer