Number theory · Digits · Factorials · Bounding · Diophantine equations
Find every three-digit number \(\overline{abc}\) whose digits \(a\), \(b\), \(c\) are all nonzero and which satisfies
\[ \overline{abc} = 3 \cdot a! + 2 \cdot b! + c! . \]
Here \(\overline{abc}\) is the number with hundreds digit \(a\), tens digit \(b\) and units digit \(c\) in base ten.
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Serbian National Competition (Drzavno takmicenje) 2022, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source