Spirograph

A spirograph is a children's toy that consists of a plastic plate with cut-out circles of various diameters and a set of smaller wheels with holes. The edges of these circles and wheels are toothed to prevent slipping. To use it, you place the plate on a sheet of paper, insert one of the toothed wheels into a chosen circular hole, and then insert a writing tool into one of the wheel's holes. As you move the wheel, the writing tool traces a beautiful spiral pattern on the paper.

Let's explore a more general scenario. Suppose the radius of the large circle is $rB$, the radius of the small circle is $rM$, and the writing tool is fixed at a distance $L$ from the center of the small circle, rotating along with it. Initially, the small circle touches the large circle at the point [rB, 0] (assuming the center of the large circle is the origin). The writing tool is positioned at [rB-rM+L, 0].

As the small circle rotates inside the large one, eventually all elements return to their starting positions. This process creates a figure with a certain number of "petals" (for instance, the illustration shows a figure with five "petals" using parameters: rB = 5, rM = 3, L = 4).

Your task is to find the number of unique pairs of integer radii $rB$ and $rM$ (rM < rB) that allow for drawing a figure with the specified number of "petals", where $rB$ does not exceed a given maximum $rMax$.