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Given an integer $n \geq 3$ , let $u_{1}, ..., u_{n}$ be pairwise coprime integers $\geq 2$ , $𝒟$ a family of nonempty proper subsets of ${1, ..., n}$ with “enough” elements, and $ε$ a function $𝒟 \to {\pm 1}$ . Does there exist at least one prime $q$ such that $q$ divides $\prod_{i \in I} u_{i} - ε (I)$ for some $I \in 𝒟$ , but it does not divide $u_{1} \dots u_{n}$ ? We answer this question in the positive when the $u_{i}$ are prime powers and $ε$ and $𝒟$ are subjected to certain restrictions.We use the result to prove that, if $ε_{0} \in {\pm 1}$ and $A$ is a set of three or more primes that contains all prime divisors of any number of the form $\prod_{p \in B} p - ε_{0}$ for...

On a theorem by Kronecker.

M.A. Ostrowski (1976)

Aequationes mathematicae

On a theorem of Bauer and some of its applications II

Andrzej Schinzel (1973)

Acta Arithmetica

On an Archimedian characterization of the circular units.

Robert F. Coleman (1985)

Journal für die reine und angewandte Mathematik

On an equation in cyclotomic numbers

Roberto Dvornicich (2001)

Acta Arithmetica

On certain continued fraction expansions of fixed period length

A. J. van der Poorten, H. C. Williams (1999)

Acta Arithmetica

On congruence topologies in number fields.

Daniel Segal, Fritz J. Grunewald (1979)

Journal für die reine und angewandte Mathematik

On cyclic cubic fields.

Francisca Cánovas Orvay (1991)

Extracta Mathematicae

On cyclotomic ℤ ₚ-extensions of real quadratic fields

Hisao Taya (1996)

Acta Arithmetica

On delta sets and their realizable subsets in Krull monoids with cyclic class groups

Scott T. Chapman, Felix Gotti, Roberto Pelayo (2014)

Colloquium Mathematicae

Let M be a commutative cancellative monoid. The set Δ(M), which consists of all positive integers which are distances between consecutive factorization lengths of elements in M, is a widely studied object in the theory of nonunique factorizations. If M is a Krull monoid with cyclic class group of order n ≥ 3, then it is well-known that Δ(M) ⊆ {1,..., n-2}. Moreover, equality holds for this containment when each class contains a prime divisor from M. In this note, we consider the question of determining...

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On A Combinatorial Problem Connected withFactorizations

On a congruence relation between Jacobi sums and cyclotomic units.

On a cyclotomic diophantine equation.

On a problem of Narkiewicz.

On a system of equations with primes

On a theorem by Kronecker.

On a theorem of Bauer and some of its applications II

On an Archimedian characterization of the circular units.

On an equation in cyclotomic numbers

On certain continued fraction expansions of fixed period length

On congruence topologies in number fields.

On cyclic cubic fields.

On cyclotomic ℤ ₚ-extensions of real quadratic fields

On delta sets and their realizable subsets in Krull monoids with cyclic class groups

On elliptic units and class number of a certain dihedral extension of degree 2l

On Elliptic Units and Class Number of a Certain Non-Galois Number Field.

On equation in S-units and the Thue-Mahler equation.

On equations in two S-units over function fields of characteristic 0

On explicit reciprocity laws. II.

On explicit relations between cyclotomic numbers

Currently displaying 1 – 20 of 61