Problem

Source: 2015 China Tst 1 Day 2 Q2

Tags: number theory, Diophantine equation



FIx positive integer $n$. Prove: For any positive integers $a,b,c$ not exceeding $3n^2+4n$, there exist integers $x,y,z$ with absolute value not exceeding $2n$ and not all $0$, such that $ax+by+cz=0$