Results 11 to 20 of about 272 (33)

Density of solutions to quadratic congruences [PDF]

, 2016
A classical result in number theory is Dirichlet's theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k>1. Building upon a proof by E.M.
Prabhu, Neha
core   +2 more sources

Zero-sum problems for abelian p-groups and covers of the integers by residue classes [PDF]

, 2009
Zero-sum problems for abelian groups and covers of the integers by residue classes, are two different active topics initiated by P. Erdos more than 40 years ago and investigated by many researchers separately since then.
Sun, Zhi-Wei
core   +2 more sources

On sequences without geometric progressions

, 2013
An improved upper bound is obtained for the density of sequences of positive integers that contain no k-term geometric progression.Comment: 4 pages; minor ...
Nathanson, Melvyn B., O'Bryant, Kevin
core   +1 more source

On simultaneous arithmetic progressions on elliptic curves [PDF]

, 2006
In this paper we study elliptic curves which have a number of points whose coordinates are in arithmetic progression. We first motivate this diophantine problem, prove some results, provide a number of interesting examples and, finally point out open ...
Garcia-Selfa, I., Tornero, J. M.
core   +2 more sources

The least common multiple of a sequence of products of linear polynomials

, 2011
Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty $, where $A$ is a constant depending on $f$.Comment: To appear in ...
A. Selberg, B. Farhi, B. Farhi, D. Hanson, Guoyou Qian, H. Davenport, M. Nair, P. Bateman, P. L. Chebyshev, Qianrong Tan, S. Hong, S. Hong, Shaofang Hong   +12 more
core   +1 more source

Monochromatic products and sums in the rationals

Forum of Mathematics, Pi
We show that every finite coloring of the rationals contains monochromatic sets of the form $\{x,y,xy,x+y\}$ .
Matt Bowen, Marcin Sabok
doaj   +1 more source

Improved bounds for arithmetic progressions in product sets

, 2015
Let $B$ be a set of natural numbers of size $n$. We prove that the length of the longest arithmetic progression contained in the product set $B.B = \{bb'| \, b, b' \in B\}$ cannot be greater than $O(n \log n)$ which matches the lower bound provided in an
Zhelezov, Dmitry
core   +1 more source

Polynomial progressions in topological fields

Forum of Mathematics, Sigma
Let $P_1, \ldots , P_m \in \mathbb {K}[\mathrm {y}]$ be polynomials with distinct degrees, no constant terms and coefficients in a general local field $\mathbb {K}$ . We give a quantitative count of the number of polynomial progressions $
Ben Krause, Mariusz Mirek, Sarah Peluse, James Wright   +3 more
doaj   +1 more source

Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms

, 2013
Let $l$ and $m$ be two integers with $l>m\ge 0$, and let $a$ and $b$ be integers with $a\ge 1$ and $a+b\ge 1$.
B. Farhi, B. Farhi, D. Hanson, G. Qian, Guoyou Qian, M. Nair, P. Bateman, P.L. Chebyshev, S. Hong, S. Hong, Shaofang Hong   +10 more
core   +1 more source

Irrational numbers associated to sequences without geometric progressions [PDF]

, 2013
Let s and k be integers with s \geq 2 and k \geq 2. Let g_k^{(s)}(n) denote the cardinality of the largest subset of the set {1,2,..., n} that contains no geometric progression of length k whose common ratio is a power of s.
Nathanson, Melvyn B., O'Bryant, Kevin
core