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

Authors

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

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.

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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.

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Published

2021-11-01

Issue

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

Section

Journal Articles

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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