Daily Archives: March 10, 2017

2017-02 Low-degree polynomial

Let \(a_1,a_2,\ldots,a_n\) be distinct points in \(\mathbb R^4\). Does there exist a non-zero polynomial \(P(x_1,x_2,x_3,x_4)\) such that
(1) the degree of \(P\) is at most \(\lceil\sqrt{5} n^{1/4}\rceil\) and
(2) \(P(a_i)=0\) for all \(i=1,2,\ldots,n\)?

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