Number theory · Divisibility rules · Concatenation · Arithmetic progressions
Let \(n \ge 3\), and suppose \(n\) consecutive odd three-digit numbers are given. Prove that these \(n\) numbers can be arranged into a sequence \(b_1, b_2, \ldots, b_n\) so that the number
\[ \overline{b_1b_2\ldots b_n}, \]
obtained by writing them one after another in decimal notation, is composite.
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Serbian Municipal Competition 2021, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source