Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progression contained in the product set B.B={bibj|bi, bj∈B} cannot be greater than O(n1+1/loglogn) an arithmetic progression of length Ω(nlogn), so the obtained upper bound is close to the optimal
AbstractIf A is a dense subset of the integers, then A+A+A contains long arithmetic progressions. Th...
AbstractGiven a density 0<σ⩽1, we show for all sufficiently large primes p that if S⊆Z/pZ has the le...
AbstractWe give a complete characterization of so-called powerful arithmetic progressions, i.e. of p...
Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progres...
Let B be a set of real numbers of size n . We prove that the length of the longest arithmetic pro...
Let B be a set of real numbers of size n . We prove that the length of the longest arithmetic pro...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
We describe efficient output-sensitive algorithms to find the longest arithmetic progression in a gi...
We describe eÆcient output-sensitive algorithms to nd the longest arithmetic progression in a given ...
122 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.In the last chapter we consid...
122 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.In the last chapter we consid...
We prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arith...
Given a density 0 < σ ≤ 1, we show for all sufficiently large primes p that if S ⊆ Z/pZ has the l...
AbstractGiven a density 0<σ⩽1, we show for all sufficiently large primes p that if S⊆Z/pZ has the le...
AbstractIf A is a dense subset of the integers, then A+A+A contains long arithmetic progressions. Th...
AbstractGiven a density 0<σ⩽1, we show for all sufficiently large primes p that if S⊆Z/pZ has the le...
AbstractWe give a complete characterization of so-called powerful arithmetic progressions, i.e. of p...
Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progres...
Let B be a set of real numbers of size n . We prove that the length of the longest arithmetic pro...
Let B be a set of real numbers of size n . We prove that the length of the longest arithmetic pro...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
We describe efficient output-sensitive algorithms to find the longest arithmetic progression in a gi...
We describe eÆcient output-sensitive algorithms to nd the longest arithmetic progression in a given ...
122 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.In the last chapter we consid...
122 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.In the last chapter we consid...
We prove that if a set is `large' in the sense of Erdős, then it approximates arbitrarily long arith...
Given a density 0 < σ ≤ 1, we show for all sufficiently large primes p that if S ⊆ Z/pZ has the l...
AbstractGiven a density 0<σ⩽1, we show for all sufficiently large primes p that if S⊆Z/pZ has the le...
AbstractIf A is a dense subset of the integers, then A+A+A contains long arithmetic progressions. Th...
AbstractGiven a density 0<σ⩽1, we show for all sufficiently large primes p that if S⊆Z/pZ has the le...
AbstractWe give a complete characterization of so-called powerful arithmetic progressions, i.e. of p...
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