Add to ORKGAbstract. It is a striking and elegant fact (proved independently by Furstenberg and Sárközy) that in any subset of the natural numbers of positive upper density there necessarily exist two distinct elements whose difference is given by a perfect square. In this article we present a new and simple proof of this result by adapting an argument originally developed by Croot and Sisask to give a new proof of Roth’s theorem. Dedicated to Steve Wainger on the occasion of his retirement 1
Cameron has introduced a natural one-to-one correspondence between infinite binary sequences and set...
ABSTRACT. Let \alpha be a real number, with \alpha>-1. We prove a general in- equality between the ...
summary:Let $M$ be a given nonempty set of positive integers and $S$ any set of nonnegative integers...
Abstract. In this note, we provide parallel expositions of two theorems of Sárközy, the qualitativ...
Abstract. We prove a quantitative version of the Polynomial Szemerédi Theorem for difference sets. ...
The following theorem of Roth established the first non-trivial case of a 20 year old conjecture of ...
AbstractErdős and Sárkőzy proposed the problem of determining the maximal density attainable by a se...
Let D(n) denote the cardinality of the largest subset of the set {1, 2,..., n} such that the differe...
Let P - 1 denote the set of primes minus . A classical theorem of A Sárkőzy says that any set of nat...
Cameron has introduced a natural one-to-one correspondence between infinite binary se-quences and se...
In this paper prove results concerning restrictions on the cardinality of the wildcard set in the de...
Mohanty and Ramasamy recently proved an interesting result that says that no other integers can be a...
Let be the power set of N. We say that a function is an upper density if, for all X, Y † N and h, k ...
AbstractFor a given set M of positive integers, a problem of Motzkin asks for determining the maxima...
AbstractLet m,n1,n2,…,nm and c be positive integers. Let A = {A1, A2, … Am} be a system of sequences...
Cameron has introduced a natural one-to-one correspondence between infinite binary sequences and set...
ABSTRACT. Let \alpha be a real number, with \alpha>-1. We prove a general in- equality between the ...
summary:Let $M$ be a given nonempty set of positive integers and $S$ any set of nonnegative integers...
Abstract. In this note, we provide parallel expositions of two theorems of Sárközy, the qualitativ...
Abstract. We prove a quantitative version of the Polynomial Szemerédi Theorem for difference sets. ...
The following theorem of Roth established the first non-trivial case of a 20 year old conjecture of ...
AbstractErdős and Sárkőzy proposed the problem of determining the maximal density attainable by a se...
Let D(n) denote the cardinality of the largest subset of the set {1, 2,..., n} such that the differe...
Let P - 1 denote the set of primes minus . A classical theorem of A Sárkőzy says that any set of nat...
Cameron has introduced a natural one-to-one correspondence between infinite binary se-quences and se...
In this paper prove results concerning restrictions on the cardinality of the wildcard set in the de...
Mohanty and Ramasamy recently proved an interesting result that says that no other integers can be a...
Let be the power set of N. We say that a function is an upper density if, for all X, Y † N and h, k ...
AbstractFor a given set M of positive integers, a problem of Motzkin asks for determining the maxima...
AbstractLet m,n1,n2,…,nm and c be positive integers. Let A = {A1, A2, … Am} be a system of sequences...
Cameron has introduced a natural one-to-one correspondence between infinite binary sequences and set...
ABSTRACT. Let \alpha be a real number, with \alpha>-1. We prove a general in- equality between the ...
summary:Let $M$ be a given nonempty set of positive integers and $S$ any set of nonnegative integers...