For fixed coprime positive integers $a,b$, define $n$ to be bad if it is not of the form $$ax+by,\enspace x,y\in\mathbb N^*$$Prove that there are finitely many bad positive integers. Also, find the sum of squares of them.
Source: IMOC 2017 N7
Tags: number theory
For fixed coprime positive integers $a,b$, define $n$ to be bad if it is not of the form $$ax+by,\enspace x,y\in\mathbb N^*$$Prove that there are finitely many bad positive integers. Also, find the sum of squares of them.