I came across the following conjecture, reading a recent paper in the Monthly, an orthogonal matrix of order $n\neq 0 \pmod 4$ has a nonnegative (up to a scalar) raw vector. It should be straight in dimensions $2$ and $3$ and much impossible for the rest. Do that make any relation within certain result.

I came across the following conjecture, reading a recent paper in the Monthly, an orthogonal matrix of order $n\neq 0 \pmod 4$ has a nonnegative (up to a scalar) row vector. It should be straight in dimensions $2$ and $3$.