MathDB

3

Part of 2022 Cono Sur

Problems(1)

Blocks in powers

Source: 2022 Cono Sur #3

8/9/2022
Prove that for every positive integer nn there exists a positive integer kk, such that each of the numbers k,k2,…,knk, k^2, \dots, k^n have at least one block of 20222022 in their decimal representation.
For example, the numbers 4202213 and 544202212022 have at least one block of 20222022 in their decimal representation.
number theoryDigitspower of number