Number theory · Digit sums · Divisibility criteria · Decimal representation
Determine all natural numbers \(n\) for which the following assertion is true:
a natural number \(x\) is divisible by \(n\) if and only if the sum of the digits of \(x\) is divisible by \(n\).
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Serbian Regional Competition 2009, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source