Can you help me with this task, please? Prove that set $F \subseteq K[x] \setminus \{0\}$ is Gröbner system if and only if such polynomial $f \in F$ exists, that $f$ divides any polynomial in F.
This task is from our previous year algebra exam and one of the hardest one I suppose.. I expect something similar this year, can you please help me solving this one to be prepared for the current exam? Will appreciate any help :)