MathDB
2^n contains abcd?

Source: Own. IMO 2022 Malaysian Training Camp 2

March 14, 2022
number theory

Problem Statement

Given a four digit string k=abcd‾ k=\overline{abcd} , a,b,c,d∈{0,1,⋯ ,9} a, b, c, d\in \{0, 1, \cdots, 9\} , prove that there exist a n<20000n<20000 such that 2n2^n contains kk as a substring when written in base 1010.
[Extra: Can you give a better bound? Mine is 1251712517]
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