Moreover, in case you missed a lecture, there are scans from the lectures of Michaelmas term and of Part 1 and Part 2 of Epiphany term, courtesy of Natasha Morrison.
(from Mmas) some solutions to Problem Sheet 2 [pdf]
(from Mmas) some solutions to Problem Sheet 3 [pdf]
(from Mmas) some solutions to Problem Sheet 4 [pdf]
Note: The discriminant in Sheet 10, Q4, is 404, rather than 2^8*3^2 (spotted by Natasha).
Challenges:First challenge (solved by Natasha Morrison, Steven Charlton and Matthew Palmer); here is Matt's very nice solution.
Second challenge (results from Robert Botcherby, Alex Kent, Caspar de Haes, Nick Byrne and Steven Charlton); here is a link to Steven's outstanding families of solutions!
There is actually a rather recent paper dealing with the background (and solution) of the problem (link provided by Natasha).
Reading material for year IV students:Appendices A and B of Stewart-Tall Algebraic number theory and Fermat's last theorem .
Here is now a library copy of Appendix A for module MATH4211 Number Theory IV (DUO password needed), and here is a similar link for interested 3rd year students, i.e. module MATH3031 Number Theory III.
Reading suggestions:Each of the following references covers most of the material in the lectures (in rather different form). Examples and motivation are taken from various sources. A good compilation of most of the material of the course (and far beyond) can be found in
A famous classic is
Here is a more recent standard reference, from a somewhat more advanced point of view
The following online notes of a course given by Milne contain a wealth of material.
Lots of details are explained in
while a very concise account of the theory can be found in
For exciting piece-wise (elementary) reading, with mostly independent sections in historical order, check out
Furthermore, here you can find a large library of links (some are already outdated, alas) to online notes (some of them in French, German, Dutch or even Greek!).
Assignments:  Set every fortnight (roughly); collected and marked only twice per term (presumably in week 4 and 8). Will be handed out successively and will then also be available here.
To hand in by Feb 08: Sheet 7, Q1), Q3), Q6)(i), (ii).
To hand in by Mar 08: Sheet 8, Q2 i), Q5 a), c), Q7); and Sheet 9, Q2) for d=-21.