BMO
Topics
These topics cover the training scope of BMO. Open a topic for study guidance and worked examples.
Divisibility and congruences, primes and factorisation, difference of squares and parity constraints, perfect-square tests, modular arithmetic (one of the most frequent topics in BMO1)
Polynomials and factorisation, sequences and summation, introduction to functional equations, classic inequalities such as AM–GM / QM–AM / Cauchy–Schwarz and equality analysis
Triangles and circles, angle chasing, similarity and congruence, area methods, cyclic quadrilaterals and power of a point, coordinate and vector methods
Counting and the pigeonhole principle, invariants and monotone quantities, graphs and colouring, game strategies and winning positions (frequent guests in BMO1 proof questions)