Diophantine equations and class numbers
نویسندگان
چکیده
منابع مشابه
Diophantine Equations and Class Numbers
The goals of this paper are to provide: (I ) sufficient conditions, based on the solvability of certain diophantine equations, for the non-triviality of the dass numbers of certain real quadratic fields; (2) sufficient conditions for the divisibility of the class numbers of certain imaginary quadratic fields by a given integer; and (3) necessary and sufficient conditions for an algebraic intege...
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We look at the relationships between class numbers of quadratic structures (orders and fields) and the solutions of exponential Diophantine equations. We conclude with necessary and sufficient conditions for a class group to have an element of a given order. 1. Notation and Preliminaries If D is a squarefree integer, then its discriminant is given by ( ) ( ) ≡ ≡/ = ∆ . 4 mod 1 if , 4 mod ...
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1°. Let R be a commutative ring with a unit element, F(x) a homogeneous polynomial of degree n in t indeterminates xi, x2, . . ., xi with coefficients in R. Let I denote the subring of the coefficients of F(x) in R; that is, the smallest ring containing all of them. We consider the existence of solutions of the diophantine equation F(x) = z(1) in R or in I. Here z is an indeterminate and m is a...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1986
ISSN: 0022-314X
DOI: 10.1016/0022-314x(86)90053-3