Question

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

Answer 1

Take n as any positive integer ..

sub. n = 3

3² -1 = 9-1 = 8 ( divisible by 8)

sub. n= 5
5² - 1 = 25 -1 = 24 ( divisible by 8)

sub. n = 7

7² - 1 = 49 -1 = 48 ( divisible by 8 )

and so on....

thus we reach to a conclusion that if n is odd then n²-1is divisible by 8

hope it helps
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Answer 2

Hi friend,
as n is a odd positive integer let n=2k+1 where k=real and positive integer.
Now let 2k+1=3 where k=1 substitute n=3 in n²-1 we get 3²-1=8 which is divisible by 8 there fore we can conclude that n²-1 is divisible by 8 when n is a odd positive integer.