IOQM & INMO
Masterclass.

IOQM & RMO Core

• Congruences & Theorems: Euler's Totient, Fermat's Little Theorem, and Wilson's Theorem.
• Diophantine Equations: Solving linear and non-linear polynomial equations over integers (Pell's equation).
• Functions: Properties of GCD/LCM, number of divisors, sum of divisors, and the Chinese Remainder Theorem.

RMO & INMO Core

• Advanced Configurations: Cyclic quadrilaterals, radical axes, and power of a point.
• Theorems: Menelaus, Ceva, Ptolemy, Stewart’s, and Pascal's theorems.
• Transformations: Homothety, spiral similarity, and geometric inversion techniques.

RMO & INMO Core

• Polynomials: Symmetric polynomials, Vieta’s formulas, and root bounds.
• Inequalities: AM-GM-HM, Cauchy-Schwarz, Jensen’s, and Muirhead’s inequalities.
• Functional Equations: Substitution techniques and identifying standard functions.

INMO Exclusive

• Advanced Counting: Bijections, Principle of Inclusion-Exclusion (PIE), and generating functions.
• Principles: Pigeonhole Principle (strong form) and the Extreme Principle.
• Graph Theory Basics: Trees, coloring problems, tournaments, and invariants.