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Show that n square -1 is divisible by 8, if n is a positive integer. Explain breifly guys plzz???

Posted by Thunder ?Yashwanth??? 6 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Ram Kushwah 6 years, 9 months ago

The question is like this:

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

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

If n = 4q + 1, then

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

If n = 4q + 3,then

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

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

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