MathDB

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.

Problem Statement