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

Question

Levine

Mathematics

20 May, 21:25

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

+4

Answers (1)

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Cullen · 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