Number theory · Divisibility · Factorials · Composite numbers · Prime factorization
Find all composite natural numbers \(n\) which do not divide the product of all natural numbers smaller than \(n\), that is, all composite \(n\) for which
\[ n \nmid 1 \cdot 2 \cdot 3 \cdots (n-1) . \]
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Serbian Regional Competition (Okruzno takmicenje) 1998, high school grade I, problem 4. The 1998 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS). Source