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ON $\boldsymbol{\theta} $-CONGRUENT NUMBERS OVER REAL NUMBER FIELDS

Published online by Cambridge University Press:  09 September 2020

SHAMIK DAS
Affiliation:
Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India
ANUPAM SAIKIA
Affiliation:
Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati-781039, Assam, India a.saikia@iitg.ac.in
Corresponding

Abstract

The notion of $\theta $ -congruent numbers is a generalisation of congruent numbers where one considers triangles with an angle $\theta $ such that $\cos \theta $ is a rational number. In this paper we discuss a criterion for a natural number to be $\theta $ -congruent over certain real number fields.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The first author has been supported by a Senior Research Fellowship from IIT Guwahati and the second author has been supported by a Professional Development Allowance from IIT Guwahati.

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ON $\boldsymbol{\theta} $-CONGRUENT NUMBERS OVER REAL NUMBER FIELDS
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