Vorobiev's theorem states that if , then , where is a Fibonacci number and means divides . The theorem was discovered by Vorobiev in 1942, but not published until 1967. It was used by Y. Matiyasevich in his negative solution to the Hilbert's tenth problem.
Note that the converse does not hold. For example, , but . The plot above shows values of for which and (black) and for which but (red).