Prove that, if a, b are prime numbers $a > b$, each containing at least two digits, then $a^4 - b^4$ is divisible by $240$. Also prove that, $240$ is the gcd of all the numbers which arise in this way.
Looking at the prime factorisation $240=(2^4)*3*5$, i know i need to prove that the given difference is divisible by each of these.
How do i proceed from here? i have no idea. Thanks.