AbstractConditions for divisibility of class numbers of algebraic number fields by prime powers are explored and linked to the existence of integer solutions of certain cyclotomic polynomials modulo a given rational integer. Several applications are provided, including a generalization of the Fermat “two-square theorem”
We explore the Bernoulli numbers: a sequence of rational numbers with connections to combinatorics, ...
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer inven...
For any square-free positive integer m, let H(m) be the class-number of the field Q(ςm+ςm-1 ), where...
AbstractConditions for divisibility of class numbers of algebraic number fields by prime powers are ...
AbstractFor a given positive integer m and an algebraic number field K necessary and sufficient cond...
Class groups---and their size, the class number---give information about the arithmetic within a fie...
In this essay, we study and comment on two number theoretical applications on prime cyclotomic field...
The determination of the class number of totally real fields of large discriminant is known to be a ...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
Abstract. In this paper, criteria of divisibility of the class number h + of the real cyclotomic fie...
AbstractLet K be an algebraic number field, of degree n, with a completely ramifying prime p, and le...
AbstractThe goals of this paper are to provide: (1) sufficient conditions, based on the solvability ...
This paper consists of three parts. One is a result on Fermat little theorem, the next is on radical...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
In [8], we have presented the history of auxiliary primes from Legendre’s proof of the quadratic rec...
We explore the Bernoulli numbers: a sequence of rational numbers with connections to combinatorics, ...
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer inven...
For any square-free positive integer m, let H(m) be the class-number of the field Q(ςm+ςm-1 ), where...
AbstractConditions for divisibility of class numbers of algebraic number fields by prime powers are ...
AbstractFor a given positive integer m and an algebraic number field K necessary and sufficient cond...
Class groups---and their size, the class number---give information about the arithmetic within a fie...
In this essay, we study and comment on two number theoretical applications on prime cyclotomic field...
The determination of the class number of totally real fields of large discriminant is known to be a ...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
Abstract. In this paper, criteria of divisibility of the class number h + of the real cyclotomic fie...
AbstractLet K be an algebraic number field, of degree n, with a completely ramifying prime p, and le...
AbstractThe goals of this paper are to provide: (1) sufficient conditions, based on the solvability ...
This paper consists of three parts. One is a result on Fermat little theorem, the next is on radical...
AbstractWe study properties of the polynomials φk(X) which appear in the formal development Πk − 0n ...
In [8], we have presented the history of auxiliary primes from Legendre’s proof of the quadratic rec...
We explore the Bernoulli numbers: a sequence of rational numbers with connections to combinatorics, ...
Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer inven...
For any square-free positive integer m, let H(m) be the class-number of the field Q(ςm+ςm-1 ), where...
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