PYTHAGOR TRIKES WITH A FIXED VALUE OF ONE OF THE COMPONENTS
The article presents the result of the study of Pythagorean triplets with a fixed value of one of the components. The concept of Pythagorean triplets as triples of natural numbers (a, b, c) satisfying the equality a ^ 2 + b ^ 2 = c ^ 2 is related to the geometric Pythagorean theorem for right-angled triangles, where the side of length c lies opposite the right angle. In the time of Pythagoras (Ⅵ century BC), only natural numbers were used. But this did not really limit their use. Indeed, the Egyptian triangle with an aspect ratio of 3: 4: 5 was actively used to build right angles by Egyptian surveyors and architects, for example, when building pyramids. Recently, they have been distracted from the geometric content of the Pythagorean triplets and their Dioavant equations. In the research work, reliable foreign sources and materials were used.