On the Pythagorean triangles with an irrational hypotenuse

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^۲+y^۲=z^n,n=۲,۳,۴,.. always has an solution (x,y,z) in integer numbers x,y,z∈Z={۰,±۱,±۲,…}.

Keywords:

Incomplete square , Pythagorean theorem , Solution in integer numbers