MathDB

Let

k

be a positive integer. Find the smallest positive integer

n

for which there exists

k

nonzero vectors

v_1,v_2,…,v_k

\mathbb{R}^n

such that for every pair

i,j

of indices with

|i-j|>1

the vectors

v_i

and

v_j

are orthogonal.
Proposed by Alexey Balitskiy, Moscow Institute of Physics and Technology and M.I.T.

Problem Statement