Question

Hey everyone ❤❤❤

If n is ab odd integers , then show that n^2-1 is divisible by 8.

please send answer fast ita urgent.

Answer 1

_______________________________

Step-by-step explanation:

Any odd integers in the form 4m + 1 or

4m + 3 for some integer m.

When n = 4m+1

=> n²-1 = (4m+1)²-1

=> n²-1 = 16m² + 8m +1-1

=> n²-1 = 8m ( 2m+1).

=> n²-1 is divisible by 8

When n= 4m+3

=> n²-1 = (4m+3)²-1

=> n²-1 = 16m² + 24m +9-1

=> n²-1 = 8 ( 2m²+3m+1)

=> n²-1 is divisible by 8

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