Question

show that n^2-1 is divisible by 8,if n is an odd number

Answer 1

Answer:

n²-1÷8

Step-by-step explanation:

let n be a odd no. 3

(3)²-1

9-1

8, divisible by 8

another ex

let 7

(7)²-1

49-1

48, divisible by 8

Answer 2

Answer:

ANSWER

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

letn=4p+3n2−1=(4p+1)2−1=16p2+8p+1−1=8p(2p+1)⇒n2−1isdivisibleby8n2−1=(4p+3)2−1=16p2+24p+9−1=16p2+24p+8=8(2p2+3p+1)⇒n2−1isdivisibleby8

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