On representations of real quadratic integers as sums of unitary fractions

Germán Benitez; Elkin Quintero Vanegas; Euro Vidal Sampaio

doi:10.5269/bspm.67322

On representations of real quadratic integers as sums of unitary fractions

Autores

Germán Benitez Universidade Federal do Amazonas https://orcid.org/0000-0003-0565-6300
Elkin Quintero Vanegas Universidade Federal do Amazonas - UFAM https://orcid.org/0000-0002-6641-0470
Euro Vidal Sampaio Universidade Federal do Amazonas

DOI:

https://doi.org/10.5269/bspm.67322

Resumo

We verify that each natural number $t>1$ can be expressed as a sum of unitary fractions of different natural numbers such that the least common multiple among them is coprime with a fixed value $v$. Using this fact, we characterize the real quadratic integers which appear in the representation of 1 as a unitary fraction sum over the real quadratic integer ring.

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Publicado

2025-12-05

Edição

v. 43 (2025)

Seção

Artigos

Licença

When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).

The journal utilize the Creative Common Attribution (CC-BY 4.0).

Como Citar

Benitez, G., Quintero Vanegas, E., & Vidal Sampaio, E. (2025). On representations of real quadratic integers as sums of unitary fractions. Boletim Da Sociedade Paranaense De Matemática, 43, 1-8. https://doi.org/10.5269/bspm.67322