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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