MathDB

M2758

Part of Kvant 2023

Problems(1)

Operations on powers of two

Source: Kvant Magazine No. 8 2023 M2758

1/9/2024
The numbers 2,4,…,21002,4,\ldots,2^{100} are written on a board. At a move, one may erase the numbers a,ba,b from the board and replace them with ab/(a+b).ab/(a+b). Prove that the last numer on the board will be greater than 1.
From the folklore
combinatoricsOperations