Question

Show that n^2-1 is divisible by 8,if 'n' is an odd positive integer.

Answer 1

any odd positive integer is of the form 4m+1 or 4m+3 for some integer m
for n = 4m+1 
n^2-1 = (4m+1)^2 - 1
        = 16m^2 + 8m
        = 8(2m^2 + m)
hence it is divisible by 8
for n = 4m+3
 n^2 - 1 = 16m^2 + 24m + 8
          = 8(2m^2 + 3m + 1)
it is also divisible by 8

Answer 2

Answer:

Step-by-step explanation:If n=3

3^2-1=8

If n=5

5^2-1=24

If n=7

7^2-1=48

Therefore n^2-1 is divisible by 8 where n is an odd positive integers..