Proof that $2^{10}+5^{12}$ is a composite number A hint or full answer will help a lot, because I have no idea what to do.
$$5^{12}+4\cdot 2^{8} = (5^6-2\cdot 5^3 \cdot 2^2+2\cdot 2^4)(5^6+2\cdot 5^3 \cdot 2^2+2\cdot 2^4)$$

Using $a^4+4b^4 =(a^2-2ab+2b^2)(a^2+2ab+2b^2)$
Hint: This can be expressed as the difference of two squares in a reasonably easy way.