Number theory · Divisibility · Decimal representation · Digit permutations
The decimal representation of a positive integer \(n\) uses only the digits \(1\), \(3\), \(7\) and \(9\), and each of these four digits appears at least once. Prove that the digits of \(n\) can be rearranged so that the resulting number is divisible by \(7\).
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Serbian Municipal Competition 2000, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source