Question

Show that n²-1 is divisible by 8, if n is an odd postive integer.​

Answer 1

Step-by-step explanation:

let n is an odd postive integer number and n²-1 is not divisible by 8.

n is an even postive integer number and n²-1 is divisible by 8.

therefore n=2x

where x is postive integer.

now

(n²-1)/8=a

where a is natural number.

{(2x)²-1}/8=a

(2x)²=8a+1

2x × 2x = 8a+1

which contradiction

because (8a+1) is not divide by 2.

hence our assumption is wrong.

so n is an odd postive integer number and n²-1 is divisible by 8.

Answer 2

Step-by-step explanation:

n = 3, n²-1 = 9-1 = 8

n = 5, n²-1 = 25-1 = 24

n = 7, n²-1 = 49-1 = 48

n = 9,11,13,15,...

n²-1 is divisible by 8. Hence it proved