MATRIX SOLUTIONS FOR THE NON-LINEAR EXPONENTIAL DIOPHANTINE EQUATION$$\left(X^a+\alpha I_q\right)^m+\left(Y^b+\beta I_q\right)^n=Z^2$$$$\alpha, \beta \in Z, a, b, m, n, q \in \mathrm{~N}, X, Y, Z \in M_q(\mathrm{~N})$$. JP Journal of Algebra, Number Theory and Applications, [S. l.], v. 65, n. 1, p. 1–20, 2025. DOI: 10.17654/0972555526001. Disponível em: https://pphmjopenaccess.com/jpjana/article/view/3106. Acesso em: 5 jan. 2026.