Qom University of TechnologyMathematics and Computational Sciences2717-27083120220201On the Pythagorean triangles with an irrational hypotenuse374124900110.30511/mcs.2021.539538.1040ENTofigAliyevProbabilistic control methodsSamirPur RizaFuzzy economics, Control Systems Institute of Azerbaijan National Academy of Sciences (ANAS), Baku, AzerbaijanJournal Article20210923The 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,…}.http://mcs.qut.ac.ir/article_249001_0b6f456d1618940e69427d9dcce51d89.pdf