Question

if n is an odd integer than show that n-1 is divisible by 8 .​

Answer 1

Answer:

yes it is divisible by 8 I think

Step-by-step explanation:

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Answer 2

Answer:

$question \: = \\ if \: n \: is \: an \: odd \: \\ integer \: than \: show \\ that \: {n}^{2} - 1 \: is \: divisible \: by \: 8. \\ answer$

We know ,

odd number in the form of (2P +1) where P is a natural number ,

so, n² -1 = (2P + 1)² -1

= 4P² + 4P + 1 -1

= 4P² + 4P

now , checking :

P = 1 then,

4P² + 4P = 4(1)² + 4(1) = 4 + 4 = 8 , it is divisible by 8.

P =2 then,

4P² + 4P = 4(2)² + 4(2) =16 + 8 = 24, it is also divisible by 8 .

P =3 then,

4P² + 4P = 4(3)² + 4(3) = 36 + 12 = 48 , divisible by 8

hence, we conclude that 4P² + 4P is divisible by 8 for all natural number .

hence, n² -1 is divisible by 8 for all odd value of n .