Number theory · Remainders · Division with remainder · Triangular numbers · Parity cases
Problem 5, 1999
A natural number \(n \geqslant 2\) is divided by each of the natural numbers \(1, 2, \ldots, n-1\) in turn, and all the remainders obtained are written down. Find every \(n\) for which the sum of the distinct remainders is equal to \(n\).
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Serbian Republic Competition (Republicko takmicenje) 1999, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source