Number theory ii 5 now integers in the same set are all congruent modulo 3. In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the uniqueprimefactorization theorem, states that every integer greater than 1 either is prime itself or is the product of prime numbers, and that this product is unique, up to the order of the factors. These notes serve as course notes for an undergraduate course in number theory. Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. Prove that there exists an increasing infinite sequence of triangular numbers i. Introduction to number theory lecture notes adam boocher 20145, edited by andrew ranicki 20156 december 4, 2015 1 introduction 21. Vinogradov elements of number theory dover publications inc. The ideals that are listed in example 4 are all generated by a single number g. We will especially want to study the relationships between different sorts of numbers. If ais not equal to the zero ideal f0g, then the generator gis the smallest positive integer belonging to a. H4fun problem with total number of divisors and primes by glenn olson. Note that these problems are simple to state just because a topic is accessibile does not mean that it is easy. The notes contain a useful introduction to important topics that need to be addressed in a course in number theory.
Prove that there exists an increasing infinite sequence of tetrahedral numbers i. It covers the basic background material that an imo student should be familiar with. Number theory naoki sato 0 preface this set of notes on number theory was originally written in 1995 for students at the imo level. 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. For the love of physics walter lewin may 16, 2011 duration. Recall that a prime number is an integer greater than 1 whose only positive factors are 1 and the number itself. We next show that all ideals of z have this property. Number theory basics nanyang technological university.1017 5 695 1100 956 1409 22 526 256 84 57 148 115 514 442 720 485 1128 1321 247 985 1120 1418 77 774 252 343 549 768 148 509