文档介绍：To Paul Erd?os,1913–1996,a friend and collaborator for 25 years, and amaster of elementary methods in number is where numbers run across your mind looking forthe is like numbers spinning in your head faster andfaster until you blow up with the !!!Then you sit back down and begin the next Nathanson [99]This book,Elementary Methods in Number Theory, is divided into I, “A ?rst course in number theory,” is a basic introduction to el-ementary number theory for undergraduate and graduate students withno previous knowledge of the subject. The only prerequisites are a littlecalculus and algebra, and the imagination and perseverance to follow amathematical argument. The main topics are divisibility and prove Gauss’s lawof quadratic reciprocity, and we determine the modulifor which primitive roots exist. There is an introduction to Fourier anal-ysis on ?nite abelian groups, with applications to Gauss sums. A chapteris devoted to onjecture, a simply stated but profound assertionabout the relationship between the additive and multiplicative propertiesof integers that is a major unsolved problem in number “?rst course” contains all of the results in number theory that areneeded to understand the author’s graduate texts,Additive Number Theory:The Classical Bases[104] andAdditive Number Theory: Inverse Problemsand the Geometry of Sumsets[103].viii PrefaceThe second and third parts of this book are more di?cult than the “?rstcourse,” and require an undergraduate course in advanced calculus or II is concerned with prime numbers, divisors, and other topics inmultiplicative number theory. After deriving properties of the basic arith-metic functions, we obtain important results about divisor functions, andwe prove the classical theorems of Chebyshev and Mertens on the distribu-tion of prime numbers. Finally, we give elementary proofs of two of the mos