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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.55 no.2 Bogotá jul./dez. 2021 Epub 31-Maio-2022
https://doi.org/10.15446/recolma.v55n2.102612
ORIGINAL ARTICLES
Ternary arithmetic, factorization, and the class number one problem
Aritmética ternaria, factorización, y el problema de número de clase uno
1Centro de Ciencias Matemáticas (UNAM), Morelia, México
Ordinary multiplication of natural numbers can be generalized to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of ‘3-primality’ -primality with respect to ternary multiplication- is defined, and it turns out that there are very few 3-primes. They correspond to imaginary quadratic fields ℚ (
), n > 0, with odd discriminant and whose ring of integers admits unique factorization. We also describe how to determine representations of numbers as ternary products and related algorithms for usual primality testing and integer factorization.
Keywords: Factorization; primality testing; quadratic fields
La multiplicación usual de números naturales se puede generalizar a una operación ternaria en consideración de volúmenes discretos de hexágonos de retícula. Con esta operación, se define una noción de ‘3-primalidad’ y resulta que hay muy pocos números que son 3-primos. Éstos corresponden a cuerpos cuadráticos imaginarios ℚ (), n > 0, de discriminante impar cuyos anillos de enteros admiten factorización única. También describimos cómo obtener representaciones de números enteros como productos ternarios y algoritmos relacionados de chequeo de primalidad y factorización ordinaria.
Palabras clave: Factorización; prueba de primalidad; campos cuadráticos
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Received: May 07, 2019; Accepted: May 27, 2021
This is an open-access article distributed under the terms of the Creative Commons Attribution License
