IIT JEE , AIEEE Forum - Mathematics , Algebra - Show that for any integer n,the no. n^4-20n^2+4 is not a prime no.

mroobm

Show that for any integer n,the no. n^4-20n^2+4 is not a prime no.

mukundmadhav

n^4-4n^2+4-16n^2
(n^2-2)^2-(4n)^2

At least two factors..

hsbhatt

To elaborate further, what is being used here is called the Sophie-Germain Identity

This factorization is often used to prove that a given expression is not a prime (unless of course one of the factors is 1)