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      The congruent number problem

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            Abstract

            The congruent number problem is the oldest unsolved major mathematical problem to date. The problem aiming to determine whether or not some given integer n is congruent, which corresponds to a Pythagorean triangle with integer sides, can be settled in a finite number of steps. However, once we permit the triangles to acquire rational values for its sides, the degree of difficulty of the task changes dramatically. In this paper a basis is developed, to produce right Pythagorean triangles with rational sides and integral area in a straightforward manner. Determining whether or not a given natural number n is congruent, is equivalent to a search through an ordered 2D array.

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            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            5 October 2021
            Affiliations
            [1 ] N.A.
            Author notes
            Article
            10.14293/S2199-1006.1.SOR-.PPKRDW5.v1
            7e9a1fcf-9bb1-436c-a645-29a44d111fa3

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


            All data generated or analysed during this study are included in this published article (and its supplementary information files).
            Mathematics
            Babylonian mathematics,Congruent numbers,Congruent Number Problem,Homogeneous Diophantine equations,Euclid’s parametrization,Pythagorean triples

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