Question

If n is an odd integer, then show that n^2-1 is divisible by 8

Answer 1

Odd number : 4m+1 or 4m+3
When n=4m+1
n²=(4m+1)²
n²-1=(4m+1)²-1
n²-1=16m²+8m+1-1
n²-1=8m(2m+1)
Therefore n²-1 is divisible by 8

similarly,when n=4m+3
n²=(4m+3)²
n²-1=(4m+3)²-1
n²-1=16m²+24m+9-1
n²-1=8(2m²+3m+1)
Therefore n²-1 is divisible by 8
So if n is an odd integer, then n²-1 is divisible by 8

Answer 2

Let the odd no are 4m+1 or 4m+3 When n=4m+1 n²=(4m+1)² n²-1=(4m+1)²-1 n²-1=16m²+8m+1-1 n²-1=8m(2m+1) Therefore n²-1 is divisible by 8 similarly,when n=4m+3 n²=(4m+3)² n²-1=(4m+3)²-1 n²-1=16m²+24m+9-1 n²-1=8(2m²+3m+1) Therefore n²-1 is divisible by 8. PLZ MARK AS A BRAINLIEST. I NEEDED PLZ MARK AS A BRAINLIEST.