Q Prove that  is composite for all integer values of n greater than 1.

 For even numbers it is obvious but I am unable to show it is composite for odd Integers.

Its easy enough for odd n also. You just have to know the Sophie Germain Identity.

Sophie Germain's Identity, states that for any two numbers x and y:

x⁴ + 4y⁴ = (x² + 2y² + 2xy)(x² + 2y² − 2xy).

Then the reqd question becomes  which is in the sophie germain form!

Thanks a lot for the answer. It is very easy to prove the identity.

Yes ofcourse. Direct factorisation. But dead useful identity!

 i have studied this identity in 9th standard

but i dint know this had a name 

you wouldnt have known the name ofc

Also this identity can be used in the most unexpected of circumstances

See an application of this identity here

http://www.goiit.com/posts/list/algebra-try-this-too-easy-47105.htm 

(By none other than yours truly )