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IMO 1981/2 via generating functions
A generating-functions proof that the average minimum of an r-subset of {1,...,n} is (n+1)/(r+1).
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SKMO 2026/1 via KKT conditions
Solving a problem from SKMO with the Karush–Kuhn–Tucker conditions.
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Infinity of primes
A group-theoretic proof of infinity of primes.
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Orbit counting lemma
A graph-theoretic proof of the orbit-counting theorem.
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Matrix recurrence for non-backtracking walks
A matrix recurrence for walks that avoid immediately retracing the last edge.