A New Proof for Congruent Number’s Problem via Pythagorician Divisors

Considering Pythagorician divisors theory which leads to a new parameterization, for Pythagorician triplets $\left(a\mathrm{,}b\mathrm{,}c\right)\in {\mathbb{N}}^{3\ast }$ , we give a new proof of the well-known problem of these particular squareless numbers $n\in {\mathbb{N}}^{\ast }$ , called congruent numbers, characterized by the fact that there exists a right-angled triangle with rational sides: ${\left(\frac{A}{\alpha }\right)}^2+{\left(\frac{B}{\beta }\right)}^2={\left(\frac{C}{\gamma }\right)}^2$ , such that its area $\Delta =\frac{1}{2}\frac{A}{}$