Both files contain identical theory notes, intended to support those training for competitions in their
preparation.
These notes collect, in a way I hope is reasonably clear and well-organized, the tools I use in the various
solutions — tools that are
typically not covered by standard high school curricula.
A - Geometry in coordinates and vectors
B - Power of a point with respect to a circle
C - Cevians
D - Notable points of a triangle
E - Quadrilaterals and inequalities between means
F - Summations & products
G - Angles that are multiples of 18 degrees
H - Burnside's lemma
I - Congruences and divisibility among integers
J - Complex numbers
K - Polynomials
L - Sequences and recurrence equations
M - Approximations and continued fractions
N - Diophantine equations
O - Binomial coefficients
P - Generating functions
Q - Partitions
R - Graph theory
S - Polyhedra
T - Lattices
U - Arithmetic functions
V - p-adic valuations
