Approximate counting via Euler transform
Approximate squaring.
Arithmetic and growth of periodic orbits.
Arithmetic functions on Beatty sequences
Arithmetic on blocks.
Arithmetic progressions and the primes.
We describe some of the machinery behind recent progress in establishing infinitely many arithmetic progressions of length k in various sets of integers, in particular in arbitrary dense subsets of the integers, and in the primes.
Arithmetic progressions formed by pseudoprimes
Arithmetic progressions in a unique factorization domain
Arithmetic progressions in sums of subsets of sparse sets
Arithmetic progressions in sumsets
1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B always contains an arithmetic progression of length . Our aim is to show that this is not very far from the best possible. Theorem 1. Let ε be a positive number. For every prime p > p₀(ε) there is a symmetric set A of residues mod p such that |A| > (1/2-ε)p and A + A contains no arithmetic progression of length (1.1). A set of residues can be used to get a set of integers in an obvious way. Observe...
Arithmetic progressions of length three in subsets of a random set
Arithmetic progressions of primitive roots of a prime. II.
Arithmetic progressions, prime numbers, and squarefree integers
In this paper we establish the distribution of prime numbers in a given arithmetic progression for which is squarefree.
Arithmetic progressions that consist only of reduced residues.
Arithmetic progressions with common difference divisible by small primes
Arithmetic properties of automata: regular sequences.
Arithmetic properties of Bell numbers to a composite modulus I
Arithmetic Properties of Generalized Bernoulli Numbers.
Arithmetic properties of members of a binary recurrent sequence
Arithmetic structures in random sets.