MathDB
Splitting piles of stones and powers of 2

Source: Tuymaada 2021/J7

July 30, 2021
combinatoricsnumber theory

Problem Statement

A pile contains 202120212021^{2021} stones. In a move any pile can be divided into two piles so that the numbers of stones in them differ by a power of 22 with non-negative integer exponent. After some move it turned out that the number of stones in each pile is a power of 22 with non-negative integer exponent. Prove that the number of moves performed was even.