prove that if n is any odd integer then 8/n^2-1 by mathematical induction?

Question

anonymous · Answer

Just replace n with 2m+1

anonymous · Answer

Well, I'd start with that at least.

anonymous · Answer

You could also try substituting n with n+1

waleed_imtiaz · Answer

can u please give me the full solution
step by step...

anonymous · Answer

Wait I don't the question is complete. You just said "prove that if n is an odd integer then 8/9^2-1"...What 8/9^2-1?

waleed_imtiaz · Answer

i said 8|n^2-1 .... 
prove by mathematical induction that for all values of n(odd integers) , the function is divisible by 8...

anonymous · Answer

Base case n = 1.  8|n^2-1 =  8|0 True
Assume  8|n^2-1
8|(n+2)^2-1 =  8| n^2+ 4n+3 =  8|n^2-1+4n+4 =  8|n^2-1+4(n+1) which is True since n^2-1 divides 8 and 4(n+1) divides 8 since n+1 is even and 4/8(n+1)=4/8*2*n=n

sirm3d · Answer

an odd number n can be represented by either
    (a) 4m+1, or
    (b) 4m+3

use mathematical induction on each case