MathDB
Diving into equal masses for rational or irrational a

Source:

February 9, 2011
rationumber theory unsolvednumber theory

Problem Statement

Alex has a piece of cheese. He chooses a positive number a and cuts the piece into several pieces one by one. Every time he choses a piece and cuts it in the same ratio 1:a1 : a. His goal is to divide the cheese into two piles of equal masses. Can he do it if (a)a(a) a is irrational? (b)a(b) a is rational, a1?a \neq 1?