Let $P_{0}, P_{1}, P_{2}, \ldots$ be non-zero orthogonal polynomials on an interval $[a, b]$ such that the degree of $P_{j}$ is equal to $j$ for every $j=0,1,2, \ldots$, where the orthogonality is with respect to the inner product $<f, g>=\int_{a}^{b} f g$. If $f$ is any continuous function on $[a, b]$ orthogonal to $P_{0}, P_{1}, \ldots, P_{n-1}$ and not identically zero, prove that $f$ must have at least $n$ distinct zeros in $(a, b)$.