Question

n^2 -I is divisible by 8 if n is​

Answer 1

Answer:

n 2 –1 is divisible by 8 if n is an odd positive integer.

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,

(n 2 –1)=(4p+1)

2 –1=16p 2+8p+1=16p

2 +8p=8p(2p+1)

⇒(n 2 –1) is divisible by 8.

(n 2–1)=(4p+3) 2 –1=16p 2 +24p+9–1=16p

2+24p+8=8(2p 2 +3p+1)

⇒n 2

–1 is divisible by 8.