Number theory · Unit fractions · Primes · Divisibility · Diophantine equations
Find all prime numbers \(p\), \(q\), \(r\), not necessarily different from one another, and all positive integers \(n\), for which
\[ \frac{1}{p} + \frac{1}{q} + \frac{1}{r} = \frac{1}{n}. \]
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Serbian Municipal Competition 2005, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source