We investigate arithmetical properties on the 0-genus algebraic structure of the hyperbola parametrized by  and study algebraic and arithmetical properties on the group structure among isomorphisms, integral solutions, and relations between integral solutions and divisors of the parameter n, and present a factorization method.

hyperbola curve, integral points, factorization, isomorphisms.

Received: September 18, 2020;  Accepted: November 20, 2020; Published: March 26, 2021

How to cite this article: Gilda Rech Bansimba, Regis Freguin Babindamana and Basile Guy Richard Bossoto, Some arithmetical properties on hyperbola, JP Journal of Algebra, Number Theory and Applications 50(1) (2021), 45-100. DOI: 10.17654/NT050010045

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