Mathematics and Computational Sciences

On the Pythagorean triangles with an irrational hypotenuse

Document Type : Original Article

Authors

Tofig Aliyev 1
Samir Pur Riza 2

1 Probabilistic control methods

2 Fuzzy economics, Control Systems Institute of Azerbaijan National Academy of Sciences (ANAS), Baku, Azerbaijan

https://doi.org/10.30511/mcs.2021.539538.1040
Abstract
The paper investigates a number of incomplete exact roots of a series of natural numbers, in relation to the Pythagorean theorem that in a right-angled triangle the square of the hypotenuse is equal to the sum of the squares of the legs. It uses the fact that the equation x^2+y^2=z^n,n=2,3,4,.. always has an solution (x,y,z) in integer numbers x,y,z∈Z={0,±1,±2,…}.

Keywords

Incomplete square
Pythagorean theorem
Solution in integer numbers
[1] T.M. Aliyev, N.A. Aliyev, K.M. Jabiyev, Mystery of finite and infinite quantities, ASPU Publishing House, Baku-2020.
[2] N.A. Aliyev, From the history of the creation of numbers, Chashyoglu Publishing House, Baku, 2020.
[3] I.L. Kantor, A.S. Solodovnikov, Hypercomplex Numbers, Russia, Moscow: Nauka, 1973.
[4] Y.V. Nesterenko, Number theory (in rus), Academy, Russia, Moscow, 272, 2008.
Mathematics and Computational Sciences
Volume 3, Issue 1
Winter 2022
Pages 37-41

  • Receive Date 23 September 2021
  • Accept Date 03 December 2021

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