Direct proof through an equilateral hyperbola to find the infinite Pythagorean triples and a direct proof to find the sum of all odd numbers through a telescopic series

Odirley Willians Miranda Saraiva; Cássio Pinho dos Reis; Antônio Thiago Madeira Beirão; Katiane Pereira Silva; Herson Oliveira da Rocha; Fabrício da Silva Lobato; Daniele Cristina de Brito Soares; Adonai do Socorro da Cruz Gonçalves; Angélica Bittencourt da Cruz Galiza; Inocêncio Renato Gasparim

doi:10.31686/ijier.vol9.iss11.3543

Direct proof through an equilateral hyperbola to find the infinite Pythagorean triples and a direct proof to find the sum of all odd numbers through a telescopic series 191 104

Authors

Odirley Willians Miranda Saraiva Universidade Regional do Noroeste do Estado do Rio Grande do Sul Author https://orcid.org/0000-0001-9090-3788
Cássio Pinho dos Reis Federal University of Mato Grosso do Sul Author
Antônio Thiago Madeira Beirão Federal Rural University of Amazonia Author https://orcid.org/0000-0003-1366-5995
Katiane Pereira Silva Federal Rural University of Amazonia Author https://orcid.org/0000-0001-7864-6467
Herson Oliveira da Rocha Federal Rural University of Amazonia Author
Fabrício da Silva Lobato State University of Pará Author https://orcid.org/0000-0002-4250-4763
Daniele Cristina de Brito Soares Federal Rural University of Amazonia Author
Adonai do Socorro da Cruz Gonçalves Federal University of Para Author
Angélica Bittencourt da Cruz Galiza Federal University of Para Author
Inocêncio Renato Gasparim SEASTER Author

DOI:

https://doi.org/10.31686/ijier.vol9.iss11.3543

Abstract

In this article a prove new properties like a connection with Pythagorean triples and a hiperbolic equation. I prove a direct proof about a serie, a telescopic series about the even sum and odd sum. I had an article that use this properties but this results is mine. I discovered this theorem and prove in this article.

References

A. Hefez, Elements of Arithmetic, SBM, 2000.

E. R. Scheinerman, Discrete Mathematics: An Introduction, Cengage Learnig, 2016.

S. Singh, Fermat's Last Theorem, Fourth State. 2002.

Downloads

Published

2021-11-01

Issue

Vol. 9 No. 11 (2021): International Journal for Innovation Education and Research

Section

Journal Articles

License

This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

Copyrights for articles published in IJIER journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author for more visit Copyright & License.

How to Cite

Saraiva, O. W. M., Reis, C. P. dos, Beirão, A. T. M., Silva, K. P., Rocha, H. O. da, Lobato, F. da S., Soares, D. C. de B., Gonçalves, A. do S. da C., Cruz Galiza, A. B. da, & Gasparim, I. R. (2021). Direct proof through an equilateral hyperbola to find the infinite Pythagorean triples and a direct proof to find the sum of all odd numbers through a telescopic series. International Journal for Innovation Education and Research, 9(11), 511-514. https://doi.org/10.31686/ijier.vol9.iss11.3543

Download Citation