# Arithmetic progressions

Xem 1-19 trên 19 kết quả Arithmetic progressions
• ### Đề tài " The primes contain arbitrarily long arithmetic progressions "

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The ﬁrst is Szemer´di’s theorem, which ase serts that any subset of the integers of positive density contains progressions of arbitrary length. The second, which is the main new ingredient of this paper, is a certain transference principle. This allows us to deduce from Szemer´di’s e theorem that any subset of a suﬃciently pseudorandom set (or measure) of positive relative density contains progressions of arbitrary length. ...

• ### Analytic Number Theory Clay Mathematics Proceedings

Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in GÃ¶ttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.

• ### Number Theory Problems (The J29 Project)

1. Show that there exist in nitely many non similar triangles such that the side-lengths are positive integers and the areas of squares constructed on their sides are in arithmetic progression. 2. Let n be a positive integer. Find the number of those numbers of 2n digits in the binary system for which the sum of digits in the odd places is equal to the sum of digits in the even places.

• ### Báo cáo toán học: "On the Structure of Sets with Few Three-Term Arithmetic Progressions"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài:On the Structure of Sets with Few Three-Term Arithmetic Progressions...

• ### Đề tài " Finite and infinite arithmetic progressions in sumsets "

We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a suﬃciently large constant, then the collection of subset sums of A contains an arithmetic progression of length n. As an application, we conﬁrm a long standing conjecture of Erd˝s and Folkman on complete sequences. o

• ### Enumerating permutations that avoid three term arithmetic progressions Arun Sharma Department of

Enumerating permutations that avoid three term arithmetic progressions Arun Sharma Department of Mathematics University of California, Berkeley Berkeley, CA 94720 asharma@math.berkeley.edu Submitted: Aug 15, 2008; Accepted: May 4, 2009; Published: May 15, 2009 Mathematics Subject Classiﬁcations: 05A15, 05C55. Abstract It is proved that the number of permutations of the set {1, 2, 3, . . . , n} that n avoid three term arithmetic progressions is at most (2.7) for n ≥ 11 and at 21 each end of any such permutation, at least ⌊ n ⌋−6 entries have the same parity. 2 1.

• ### Báo cáo toán học: "On rainbow arithmetic progressions"

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: On rainbow arithmetic progressions...

• ### Báo cáo toán học: "Discrepancy of Cartesian Products of Arithmetic Progressions"

Tuyển tập các báo cáo nghiên cứu khoa học trên tạp chí toán học quốc tế đề tài: Discrepancy of Cartesian Products of Arithmetic Progressions...

• ### Báo cáo toán học: "Sets of integers that do not contain long arithmetic progression"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Sets of integers that do not contain long arithmetic progressions...

• ### Báo cáo toán học: " Triangle Free Sets and Arithmetic Progressions – Two Pisier Type Problems'

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Triangle Free Sets and Arithmetic Progressions – Two Pisier Type Problems...

• ### Báo cáo toán học: "Thue-like sequences and rainbow arithmetic progressions Jaroslaw Grytczuk"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: Thue-like sequences and rainbow arithmetic progressions Jaroslaw Grytczuk

• ### Báo cáo toán học: "Discrepancy of Sums of Three Arithmetic Progressions"

Tuyển tập các báo cáo nghiên cứu khoa học về toán học trên tạp chí toán học quốc tế đề tài: Discrepancy of Sums of Three Arithmetic Progressions...

• ### Analytic Number Theory A Tribute to Gauss and Dirichlet William Duke Yuri Tschinkel Editors

Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.

• ### Independent And Stationary Sequences Of Random Variables - Chapter 4

Chapter 4 LOCAL LIMIT THEOREMS § 1. Formulation of the problem Suppose that the independent, identically distributed random variables X1 , X2 ,. . . . have a lattice distribution with interval h, so that the sum Zn = X1 + X2 + . . . + X„ takes values in the arithmetic progression {na + kh ; k = 0, ± 1, . . . } .

• ### Ebook Higher engineering mathematics (5th edition): Part 1

(BQ) Part 1 book "Higher engineering mathematics" has contents: Algebra, inequalities, hyperbolic functions, arithmetic and geometric progressions, partial fractions, the binomial series, logarithms and exponential functions, the binomial series,...and other contents.

• ### The Arithmetic of Fundamental Groups

Mathematical theories and methods and effective computational algorithms are crucial in coping with the challenges arising in the sciences and in many areas of their application. New concepts and approaches are necessary in order to overcome the complexity barriers particularly created by nonlinearity, high-dimensionality, multiple scales and uncertainty. Combining advanced mathematical and computational methods and computer technology is an essential key to achieving progress, often even in purely theoretical research.

• ### Đề tài " Nonconventional ergodic averages and nilmanifolds "

We study the L2 -convergence of two types of ergodic averages. The ﬁrst is the average of a product of functions evaluated at return times along arithmetic progressions, such as the expressions appearing in Furstenberg’s proof of Szemer´di’s theorem.

• ### Đề tài " Roth’s theorem in the primes "

We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes. 1. Introduction Arguably the second most famous result of Klaus Roth is his 1953 upper bound [21] on r3 (N ), deﬁned 17 years...