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Supervisors Project Submission Form Supervisor: M D Coleman 1 Project Title Fermat's Last Theorem for regular primes. 2 Category Pure 3 Level 3/4 4 Semesters 2 5 Description 6 References Follow Stewart and Tall's book (preferably the 3rd edition, though the 2nd will suffice) to prove Kummer's special case of Fermat's Last Theorem when the exponent n in x^n + y^n = z^n is a “regular" prime. Looking at the chapter headings in the main reference [1] we find Algebraic numbers, quadratic and cyclotomic number fields, factorization, ideals, Minkowski's Theorem, Class-goups and class numbers. Only a selection of these topics will be covered in detail. 1. Stewart, I.N. and Tall, D.O. Algebraic Number Theory, Chapman and Hall [In the 3rd edition the main result is Theorem 11.4.] 2. Edwards, H.M. Fermat's Last Theorem, Springer-Verlag, Graduate Texts in Mathematics 50. [Up to Chapter 5]. 7 Prerequisite courses 8 Additional notes

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