Here is a problem from Ernst Kunz's Introduction to Commutative Algebra and Algebraic Geometry:
Let $K$ be an infinite field, $V \subset \mathbb{A}^n(K)$ a finite set of points. It's ideal $\mathfrak{J}(V)$ in $K[X_1, ..., X_n]$ is generated by $n$ polynomials. Hint: Interpolation.
note: $\mathfrak{J}(V)$ consists of all $F \in K[X_1, ..., X_n]$ with $F(x) = 0$ for all $x\in V$
A similar question can be found in enter link description here. The solutions given above are not complete and satisfying. I've tried some simple cases: $n = 1$ and $V$ is a single point. For other cases, I don't have any accessible solutions.
Anyone can help? Prefect the solution in the link or give an alternative approach to the problem. Thank you!