elementary number theory - clark
elementary number theory - clark
... divisor of both a and a +1is1. Elementary Number Theory W. Edwin Clark Department of Mathematics University of South Florida Revised June 2, 2003 Copyleft 2002 by W. Edwin Clark Copyleft means that ... triangular number t n is the number of dots in a triangular array that has n rows with i dots in the i-th row. Find aformulafort n , n ≥ 1. (b) Suppose that for each n ≥ 1. Let s...
Ngày tải lên: 31/03/2014, 16:21
Elementary Number Theory: Primes, Congruences, and Secrets pdf
... [LL93]), which is the best-known general purpose factoriza- tion algorithm. A description of how the number field sieve works is beyond the scope of this book. However, the number field sieve makes ... There are infinitely many composite num- bers. Proof. To obtain a new composite number, multiply together the first n composite numbers and don’t add 1. 12 1. Prime Numbers 1.2.2 Enumerating P...
Ngày tải lên: 07/03/2014, 16:20
elementary number theory and primality tests
... natural numbers N are well-ordered, ie every subset S ⊂ N has a least element. 1.4 The Fundamental Theorem of Arithmetic Proposition 1.4 (Euclid’s Lemma) Suppose p ∈ N is a prime number; and sup- pose ... coprime to n even if n is composite. 5.2 Carmichael numbers Definition 5.2 Suppose n is an odd number > 1. Then we say that n is aCarmichael number if n is not a prime, but is a pseud...
Ngày tải lên: 31/03/2014, 16:21
elementary number theory notes - santos
... Arithmetic-Mean-Geometric-Mean Inequality for n = 2. Assume that the Arithmetic-Mean-Geometric-Mean Inequality holds true for n = 2 k−1 , k > 2, that is, assume that nonnegative real numbers ... (Arithmetic-Mean-Geometric-Mean Inequality) Let a 1 , a 2 , . . . , a n be nonnegative real numbers. Then n √ a 1 a 2 ···a n ≤ a 1 + a 2 + ···+ a n n . Proof Since the square of any real number i...
Ngày tải lên: 31/03/2014, 16:21
elementary methods in number theory - nathanson m.b
... picture. ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣rrrrrrr❜❜ -2 1 -1 4 -7 0 7 14 21 -1 6 16 The principle of mathematical induction states that if S(k) is some state- ment about integers k ≥ k 0 such that S(k 0 ) ... nonempty set of k-tuples of positive inte- gers contains a smallest element. 1.2 Greatest Common Divisors Algebra is a natural language to describe many results in...
Ngày tải lên: 31/03/2014, 16:21
Tài liệu Frontiers in Number Theory, Physics, and Geometry II docx
... Take a holomorphic theory with field space F hol , and the complex conjugate of the n-point functions. This is a theory of anti-holomorphic fields, with a field space F hol anti-linearly isomorphic ... holomorphic theory with Virasoro field T and G ⊂ F a theory with Virasoro field T 1 , then the complementary sub -theory G has a Virasoro field T −T 1 . Consider now the holomorphic field...
Ngày tải lên: 12/02/2014, 16:20
Tài liệu Frontiers in Number Theory, Physics, and Geometry I ppt
... work of Conrey-Ghosh, Conrey-Gonek, Duke-Friedlander-Iwaniec, Kowalski-Michel-Vanderkam, Ju- tila, Motohashi, Ivic, Soundararajan, Rubinstein, and others on moments of families of L-functions which ... conjectures of Keating-Snaith and Conrey-Farmer on moments of zeta- and L-functions and another was the development of the notion of symmetry type of families of L- functions by Katz-Sarnak. Ad...
Ngày tải lên: 12/02/2014, 17:20
Solved and unsolved problems in number theory daniel shanks
... = IU. (3112k - 1) = -1 ’(12k - 113)R = -1 . (-1 13)p = IN (3112k + 5) = (1% + 513)R = (-1 13)p = -IN. (3112k - 5) = -1 (12k - 513)R = -1 .(113)p = -lo. Therefore q ... in number theory . Bibliography: p . Includes index . 1 . Numbers. Theory of . I . Title . [QA241.S44 19781 5E.7 7 7-1 3010 ISBN 0-8 28...
Ngày tải lên: 15/03/2014, 16:03