Journal of the Ramanujan Mathematical Society

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A Cubic Generalization of Brahmagupta’s Identity


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1 School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland, 4072, Australia
     

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We give an algebraic identity for cubic polynomials which generalizes Brahmagupta’s identity and facilitates arithmetic in cubic fields. We also pose a question about a relationship between the elements of a cubic field of fixed trace and fixed norm and rational points of an elliptic curve.
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  • A Cubic Generalization of Brahmagupta’s Identity

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Authors

Samuel A. Hambleton
School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland, 4072, Australia

Abstract


We give an algebraic identity for cubic polynomials which generalizes Brahmagupta’s identity and facilitates arithmetic in cubic fields. We also pose a question about a relationship between the elements of a cubic field of fixed trace and fixed norm and rational points of an elliptic curve.