A Mathematical Olympiad Companion 【GENUINE - 2026】

Olympiad problems draw from four core fields—algebra, combinatorics, number theory, and geometry. Yet the tools required go far beyond the standard curriculum. A companion begins by acknowledging this gap. It introduces modular arithmetic not as a curiosity, but as a scalpel for Diophantine equations. It explains the Cauchy-Schwarz inequality not as a formula, but as a lens to see hidden relationships. It demystifies invariants, extremal principles, and generating functions, transforming them from "tricks" into systematic methods.

In a typical math book, you see a problem, and then you see a sleek, elegant solution. This often creates a misleading impression: that the solver simply looked at the problem and instantly knew the path forward. a mathematical olympiad companion

The term often refers to , published by the United Kingdom Mathematics Trust (UKMT). As a sequel to the A Mathematical Olympiad Primer , this book serves as a more advanced guide for students who have already mastered basic competition techniques and are ready to tackle harder problems. It introduces modular arithmetic not as a curiosity,