The matrix diophantine equations $AX + BY = C$

N. S. Dzhaliuk, V. M. Petrychkovych


A method of constructing of solutions of matrix Diophantine equations $AX + BY = C$ over commutative domains of finitely generated principal ideals is suggested. The formulas of general solutions of such equations in some cases is proposed. The criterion of uniqueness in the proper sense of their solutions is established.

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