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APMO – Selected topics

10 topics built from all Asian Pacific Mathematics Olympiad (APMO) papers 1989–2026: key ideas with pictures, 50 fully worked proofs and the real APMO problems of each topic for proof practice.

Inequalities

Polynomials, equations and sequences

Functional equations

Divisibility, primes and congruences

Diophantine equations and representations of integers

Triangle geometry: lengths, angles and areas

Circles, cyclic quadrilaterals and tangents

Counting and extremal combinatorics

Combinatorial geometry and graphs

Games, invariants and processes

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