MathDB

Alice has an integer

N > 1

on the blackboard. Each minute, she deletes the current number

x

on the blackboard and writes

2x+1

x

is not the cube of an integer, or the cube root of

x

otherwise. Prove that at some point of time, she writes a number larger than

10^{100}

.
Proposed by Anant Mudgal and Rohan Goyal

Problem Statement