Some notes and problems on finding and solving recurrence relations. Read these if you’ve ever wondered how to find a formula for the Fibonacci sequence!
These notes by Arkadii Slinko explain how to extract information from symmetric polynomials of a set of variables, and how to break any symmetric polynomial down into a few simple ones. The final section gives some applications to triangle geometry.
These notes by Arkadii Slinko cover techniques — some standard, some exotic — for solving functional equations: groups of substitutions, commutativity, the Cauchy functional equation.
Solutions to some of the problems are available, and can be obtained by writing to nzmathsolymp@gmail.com.
This series of short introductory articles by Arkadii Slinko covers some of the most fundamental results in number theory.
Tutorial 1: Divisibility and Primes
Tutorial 2: The Euclidean Algorithm
Tutorial 3: Euler’s Function
Tutorial 4: Primes that are Sums of Two Squares
Tutorial 5: Bertrand’s Theorem
(Update, 24/1/09: some typos fixed.)
Notes from Heather Macbeth’s algebra lecture at the January 2009 camp.
(Updated, 12/4/2010)
These notes by Arkadii Slinko outline a number of techniques for solving Diophantine equations.
Solutions for some of the problems are available, and can be obtained by writing to nzmathsolymp@gmail.com.
(Update, 24/1/2009: some typos fixed.)