Number theory · Least common multiple · Prime powers · Exponential diophantine equations
For a positive integer \(n\), let \(f(n)\) denote the least common multiple of the numbers \(1, 2, \ldots, n\). Find all positive integers \(n\) for which
\[ f(n) < f(n+1) < f(n+2) < f(n+3) . \]
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Serbian National Competition (Drzavno takmicenje) 2023, high school grade I, category A, problem 3. Organized by the Mathematical Society of Serbia (DMS). Source