From Diofantian Equations to Matricial Equations (I) - Equations and Pythagorean Matrices

We propose, starting with this work, presenting a way to achieve a systemic vision of a certain mathematical notional content, vision to motivate and mobilize the work of those who teach in class, thus facilitating teaching and assimilation of notions, concepts, scientific theories approached by educational disciplines that present phenomena and processes in nature. We present here a systemic approach to solving a Diophantine equation, namely a Pythagorean equation in the set of natural numbers, then in Z, to then "submerged" such an equation in a ring of matrices and try to find as many matrices solutions as possible. Thus, first we will present a didactic solution to the Pythagorean equation, after which we will determine all the matrix solutions of such an equation in the M ring. These matrices will be called pitagorean matrices. We will limit ourselves only to the second-order matrices, because for larger matrices the calculations are more and more complicated. But we will also present matrix solutions of at least 3.