$n\in \mathbb{N}$ is called “good”, if $n$ can be presented as a sum of the fourth powers of five of its divisors (different). a) Prove that each good number is divisible by 5; b) Find a good number; c) Does there exist infinitely many good numbers?
Problem
Source: VIII International Festival of Young Mathematicians Sozopol 2017, Theme for 10-12 grade
Tags: number theory