On the Pythagorean triangles with an irrational hypotenuse

Document Type : Original Article


1 Probabilistic control methods

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


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,…}.


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