M3P14: Elementary Number Theory
Tue 11-12 in Huxley 340, Thu 12-1 in Huxley 139, Fri 12-1 in Huxley 340
Dr. David Helm
Office Hours: Tue 1-3
This course is an introduction to elementary number theory. We will study topics
including factorization, the distribution of primes, and modular arithmetic, as
well as some simple diophantine equations.
T. Apostol, Introduction to analytic number theory
K. Rosen, Elementary number theory and its applications (this suffers from unfortunate "edition bloat";
earlier editions are generally preferable)
K. Ireland and M. Rosen, A classical introduction to modern number theory (this is somewhat more
advanced than the first two)
I am grateful to Robert Rouse for making his lecture notes
available online. They are now complete and up to date as of 13/03/2015.
Example Sheets will be posted here every two weeks. They will not be assessed work, but they will be
collected, two weeks after being assigned, and marked. This is purely optional if you want feedback
on the assignments.
Example Sheet 1 (Due Friday 31 October)
Example Sheet 2 (Due Friday 14 November)
Example Sheet 3 (Due Friday 28 November)
Example Sheet 4 (Due Friday 12 December)
The mastery material for fourth-year students in this course is about the ring of p-adic integers
and Hensel's Lemma, and is based on these notes.
These notes contain many exercises; they will not be assessed, but they are essential to understanding
the subject. Most of the exercises are straightforward; the one that is not is marked as optional and will
not be examinable material. I will be happy to answer questions (within reason) about the material (in particular,
if you think you have found a mistake or typo, please let me know.)