M2783

Part of Kvant 2024

Problems(1)

Sum of digits bounding

Source: Kvant Magazine No. 2 2024 M2783

The sum of the digits of a natural number is

k{}.

What is the largest possible sum of digits for [*] the square of this number; [*]the fourth power of this number, given that

k\geqslant 4.

From the folklore

number theorysum of digits