Anyone ?

Motivation: Bezout's Identity. Solution: Might be coming!

This simple solution was provided by me and Alireza Amiri. Note that $ax^2+bx\ge 0$ specifically for $|x|>1$ we have that $ax^2+bx\ge a|x|\ge 30$ (since $a>14$ and $|x|\ge 2$). Hence for $n<30$ we must have $|x|,|y|,|z|\leq 1$ which means they can be only $1,0,-1$ and this yields at most 27 different values between $1$ and $29$ which means there exists $n<30$ which can't be represented as the mentioned form.