Archive for the ‘Number Theory’ Category

Bertrand’s Postulate

Wednesday, August 19, 2009 8:43
Posted in category Notes, Number Theory

The fact that, for every positive integer n, there is a prime between n and 2n is known as Bertrand’s postulate (which is a bit odd, as it’s a theorem, but anyhow …) It arises occasionally in Olympiad style problems (usually with the note “You may assume Bertrand’s Postulate that …”) Michael Nielsen has a nice post giving an elementary proof at the Polymath wiki.


Number theory texts

Tuesday, February 24, 2009 16:26
Posted in category Links, Number Theory

(At least!) a couple of good, comprehensive introductions to elementary number theory are available online.  These notes by Jim Hefferon and W. Edwin Clark are nicely written and gently-paced.  These ones by Naoki Sato are a bit more Olympiad-focused.

Number theory tutorials

Tuesday, January 20, 2009 23:23
Posted in category Number Theory

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.)

Techniques for Diophantine equations

Wednesday, January 14, 2009 21:05
Posted in category Number Theory

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

(Update, 24/1/2009:  some typos fixed.)