Number theory · Digit products · Diophantine equations · Size bounds
For a natural number \(n\), let \(P(n)\) denote the product of all digits of \(n\). Find every natural number \(n\) satisfying
\[ n = P(n) + 18 . \]
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Serbian Regional Competition (Okruzno takmicenje) 2015, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source