Polynomials with roots modulo every integer

TL;DR: In this article, the smallest characteristic factor and a limit formula for the multiple ergodic averages associated to any family of three polynomials and polynomial families of the form (l_1p,l_2p,..., l_kp) were derived.

TL;DR: In this paper, it was shown that for any m > 1, every finite solvable group that is a union of conjugates of m proper subgroups occurs as the Galois group of such a polynomial, and that the same result holds for all Frobenius groups.

TL;DR: For intersective polynomials, the result of as discussed by the authors holds for the Chen primes, where a Chen prime is a prime number p such that p + 2 is the product of at most 2 primes.

TL;DR: The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press, to preserve the original texts of these important books while presenting them in durable paperback editions.

TL;DR: In this article, a discussion of hundreds of open questions, organized into 185 different topics, represent aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous.

TL;DR: In this paper, Dedekind Domains and Valuations have been used to define the theory of P-adic fields and to define a local compact Abelian group. But they do not consider the relation between the two types of fields.