- #1

Math100

- 783

- 220

- Homework Statement
- Establish the following statement:

Every integer of the form n^4+4, with n>1, is composite.

- Relevant Equations
- None.

Proof: Suppose a=n^4+4 for some a##\in\mathbb{Z}## such that n>1.

Then we have a=n^4+4=(n^2-2n+2)(n^2+2n+2).

Note that n^2-2n+2>1 and n^2+2n+2>1 for n>1.

Therefore, every integer of the form n^4+4, with n>1, is composite.

Then we have a=n^4+4=(n^2-2n+2)(n^2+2n+2).

Note that n^2-2n+2>1 and n^2+2n+2>1 for n>1.

Therefore, every integer of the form n^4+4, with n>1, is composite.