MathDB
Blocks in powers

Source: 2022 Cono Sur #3

August 9, 2022
number theoryDigitspower of number

Problem Statement

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.
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