Number theory · Digit sums · Digit products · Decimal representation · Induction
For a natural number \(n\), let \(S(n)\) be the sum of its decimal digits and \(P(n)\) the product of its decimal digits. Find all natural numbers \(n\) for which
\[ S(n) + P(n) = n . \]
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Serbian Republic Competition (Republicko takmicenje) 2002, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source