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For matrix linear equations AX + BY = C and AX + YB = C over quadratic rings ℤk$$ \mathbb{Z}\left[\sqrt{k}\right] $$, we establish necessary and sufficient conditions for the existence… Click to show full abstract
For matrix linear equations AX + BY = C and AX + YB = C over quadratic rings ℤk$$ \mathbb{Z}\left[\sqrt{k}\right] $$, we establish necessary and sufficient conditions for the existence of integer solutions, i.e., solutions X and Y over the ring of integers ℤ$$ \mathbb{Z} $$. We also present the criteria of uniqueness of the integer solutions of these equations and the method for their construction.
Keywords:
integer solutions;
equations quadratic;
matrix linear;
solutions matrix;
linear unilateral;
quadratic rings
Journal Title: Journal of Mathematical Sciences
Year Published: 2017
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Journal Title: Journal of Mathematical Sciences
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!