The Erdös sum of reciprocals conjecture is the statement that whenever A is a set of positive integers and ∑∈A 1/x = ∞, A contains arbitrarily long arithmetic progressions. It is shown here that this conjecture is equivalent to each of several other statements. Some of these other statements are combinatorial in nature while others are topological-algebraic statements
A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithm...
Erdős conjectured that for any set A of natural numbers with positive lower asymptotic density, ther...
Followed two different proofs of van der Waerden\u27s theorem. Found that the two proofs yield impo...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
Funding: JMF acknowledges financial support from an EPSRC Standard Grant (EP/R015104/1) and a Leverh...
A famous theorem of Szemerédi asserts that given any density 0 < δ ≤ 1 and any integer k ≥ 3, any...
The main goal of this project was study a topological path for number theory, specially the Erds-Tur...
The main goal of this project was study a topological path for number theory, specially the Erds-Tur...
In 1936, Erdős–Turán conjectured that any set of integers with positive upper density contains arbit...
AbstractLet A be a set of nonnegative integers such that dL(A) = w > 0. Let k be the least integer s...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a sufficient...
Followed two different proofs of van der Waerden\u27s theorem. Found that the two proofs yield impo...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithm...
Erdős conjectured that for any set A of natural numbers with positive lower asymptotic density, ther...
Followed two different proofs of van der Waerden\u27s theorem. Found that the two proofs yield impo...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
Funding: JMF acknowledges financial support from an EPSRC Standard Grant (EP/R015104/1) and a Leverh...
A famous theorem of Szemerédi asserts that given any density 0 < δ ≤ 1 and any integer k ≥ 3, any...
The main goal of this project was study a topological path for number theory, specially the Erds-Tur...
The main goal of this project was study a topological path for number theory, specially the Erds-Tur...
In 1936, Erdős–Turán conjectured that any set of integers with positive upper density contains arbit...
AbstractLet A be a set of nonnegative integers such that dL(A) = w > 0. Let k be the least integer s...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a sufficient...
Followed two different proofs of van der Waerden\u27s theorem. Found that the two proofs yield impo...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
We prove results in arithmetic combinatorics involving sums of prime numbers and also some variants ...
A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithm...
Erdős conjectured that for any set A of natural numbers with positive lower asymptotic density, ther...
Followed two different proofs of van der Waerden\u27s theorem. Found that the two proofs yield impo...
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