Question

How many whole numbers are there, whose squares and cubes have the same number of digits?

Answer 1

the answer if 4 numbers

(sorry i dont have an explenation i litterally guessed it when I entered it in the RSM portal.)

Explanation:

Answer 2

There are the following numbers for which that holds:

{-4, -2, -1, 0, 1, 2, 4}

See table below. For larger than 5 it can be proved that the number of digits will never be the same.

x x^2 x^3

0 0 0

1 1 1

2 4 8

4 16 64