In this paper we consider an analogue of the problem of Erdos and Woods for arithmetic progressions. A positive answer follows from the abc conjecture. Partial results are obtained unconditionally
122 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2000.In the last chapter we consid...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B alway...
A long standing and almost folkloric conjecture is that the primes contain arbitrarily long arithmet...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
Let a1, a2,. be a sequence of integers and let D = {d1…d2} be a fixed finite set of integers. For ea...
A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithm...
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ...
We describe some of the machinery behind recent progress in establish-ing infinitely many arithmetic...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
Let b ≥ 2 be a fixed integer. Let sb(n) denote the sum of digits of the nonnegative integer n in the...
AbstractWe give a complete characterization of so-called powerful arithmetic progressions, i.e. of p...
Dedicated to Professor R. Tijdeman on the occasion of his sixtieth birthday Abstract. We show that t...
We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a sufficient...
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...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B alway...
A long standing and almost folkloric conjecture is that the primes contain arbitrarily long arithmet...
Abstract. A long standing and almost folkloric conjecture is that the primes contain arbitrarily lon...
Let a1, a2,. be a sequence of integers and let D = {d1…d2} be a fixed finite set of integers. For ea...
A celebrated and deep result of Green and Tao states that the primes contain arbitrarily long arithm...
We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ...
We describe some of the machinery behind recent progress in establish-ing infinitely many arithmetic...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
Let b ≥ 2 be a fixed integer. Let sb(n) denote the sum of digits of the nonnegative integer n in the...
AbstractWe give a complete characterization of so-called powerful arithmetic progressions, i.e. of p...
Dedicated to Professor R. Tijdeman on the occasion of his sixtieth birthday Abstract. We show that t...
We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a sufficient...
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...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B alway...
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