Let $a$, $b$ and $c$ be given positive integers which are two by two coprime. A positive integer $n$ is called sozopolian, if it can’t be written as $n=bcx+cay+abz$ where $x$, $y$, $z$ are also positive integers. Find the number of sozopolian numbers as a function of $a$, $b$ and $c$.
Problem
Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade
Tags: number theory