Question

If n is an odd integer then n2-1 is divided by_____________ WITH EXLAINATION

Answer 1

Answer:

hope your question is n^2-1 then its divisible by 8

Step-by-step explanation:

{consider}

any positive odd integer is in the form of [ 4p + 1 ] or [ 4p + 3 ] for some integer 'p'

let n = 4p + 3

n^2 - 1  = [ 4p + 1 ] ^2 - 1  = 16p^2 + 8p + 1 - 1  = 8p [ 2p + 1 ]

; n^2 is divisible by 8

n^2 - 1 = [ 4p +3 ]^2 -1 = 16p^2 + 24p + 9 - 1 = 16p^2 + 24 + 8

8[ 2p^2 + 3p + 1 ]

therefore n^2-1 is divisible by 8 if n is a positive odd integer.

hope this answer helps you ..