We are given two positive integers p and q.Step by step, a rope of length 1 is cut into smaller pieces as follows: In each step all the currently longest pieces are cut into two pieces with the ratio p:q at the same time.
After an unknown number of such operations, the currently longest pieces have the length x.Determine in terms of x the number a(x) of different lengths of pieces of rope existing at that time. rationumber theorycombinatorics