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PAMO 2003 Problem 3

  • Day 1

Does there exists a base in which the numbers of the form: 10101,101010101,1010101010101,⋯10101, 101010101, 1010101010101,\cdots are all prime numbers?

Dataset text AI-MO AoPS. Quoted with source.

Official text: Pan-African Mathematics Olympiad 2003 official paper, page 1.

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