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Miklós Schweitzer 2003, Problem 5

Source: Miklós Schweitzer 2003

July 30, 2016
college contestsMiklos Schweitzervector

Problem Statement

Let d>1d>1 be integer and 0<r<120<r<\frac12. Show that there exist finitely many (depending only on d,rd,r) nonzero vectors in Rd\mathbb{R}^d such that if the distance of a straight line in Rd\mathbb{R}^d from the integer lattice Zd\mathbb{Z}^d is at least rr, then this line is orthogonal to one of these finitely many vectors.
(translated by L. Erdős)
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