Transcription of A Course on Number Theory
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A Course on Number Theory
A Course on Number Theory Peter J. Cameron ii Preface These are the notes of the Course MTH6128, Number Theory , which I taught at Queen Mary, University of London, in the spring semester of 2009. There is nothing original to me in the notes. The Course was designed by Su- san McKay, and developed by Stephen Donkin, Ian Chiswell, Charles Leedham- Green, and Thomas M uller; I have benefited greatly from Ian Chiswell's notes, which I have followed closely. I am grateful to Mark Walters who stood in for me in the first six lectures of the Course , and whose comments have been very helpful; also to the class tutors, markers, and most of all the students who took the Course , for their comments and support.
a natural number n, if n is prime, then it is the product of just one prime. (This starts the induction at n = 2, and is also part of the inductive step.) Otherwise, n has a factorisation n=ab with a,b<n. By the induction hypothesis (since both a and b are greater than 1 but smaller than n), they have factorisations into primes;
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