Bundeswettbewerb Mathematik 1974 Problem 2.4
Source: Bundeswettbewerb Mathematik 1974 Round 2
October 16, 2022
number theorydivisoroddremainder
Problem Statement
Peter and Paul gamble as follows. For each natural number, successively, they determine its largest odd divisor and compute its remainder when divided by . If this remainder is , then Peter gives Paul a coin; otherwise, Paul
gives Peter a coin. After some time they stop playing and balance the accounts. Prove that Paul wins.