Digit Counts of Cubes

★ 6/10number theory Modular Arithmetic Number Bases

Problem

A positive integer $a$ has $n$ digits in base ten, and $a^3$ has $m$ digits. Determine which of the values

n + m = 2020, \quad 2021, \quad 2022, \quad 2023

are possible, with proof.

Answer

Solution

Difficulty	6/10
Topics	number theory, Modular Arithmetic, Number Bases

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