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

Question

Mathematics

Brayan Horn

20 September, 07:12

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

+5

Answers (1)

Know the Answer?

Gilberto Gillespie · Answer 1

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