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an infinite sequence

Source: Mathematics Regional Olympiad of Mexico Southeast 2018 P4

October 24, 2021
number theoryinfinity

Problem Statement

For every natural nn let an=20…018a_n=20\dots 018 with nn ceros, for example, a1=2018,a3=200018,a7=2000000018a_1=2018, a_3=200018, a_7=2000000018. Prove that there are infinity values of nn such that 20182018 divides ana_n
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