Question

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

Answer 1

Answer:

Step-by-step explanation:

Any odd positive integer is in the form of 4p + 1 or 4p+ 3 for some integer p.

 

Let n = 4p+ 1,

 

(n2 – 1) = (4p + 1)2 – 1 = 16p2 + 8p + 1 = 16p2 + 8p = 8p (2p + 1)

⇒ (n2 – 1) is divisible by 8.

 

(n2 – 1) = (4p + 3)2 – 1 = 16p2 + 24p + 9 – 1 = 16p2 + 24p + 8 = 8(2p2 + 3p + 1)

⇒ n2– 1 is divisible by 8.

Therefore, n2– 1 is divisible by 8 if n is an odd positive integer.

Answer 2

if n is an odd number , then show that n square -1 is divisible by 8..
for proving this ,
take an odd number (n)=3

then , n square - 1 = (3*3)-1
=(9)-1
=8

here 8 is divisible by 8

so hence proved,....

HOPE IT HELPS YOU BUDDY❤