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n such that 1010... 101 is prime

Source: XIV May Olympiad (Olimpiada de Mayo) 2008 L2 P3

September 19, 2022
number theoryprime

Problem Statement

In numbers 1010...1011010... 101 Ones and zeros alternate, if there are nn ones, there are n−1n -1 zeros (n≥2n \ge 2 ).Determine the values of nn for which the number 1010...1011010... 101, which has nn ones, is prime.
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