Integer Solutions of Matrix Linear Unilateral and Bilateral Equations over Quadratic Rings
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DOI: 10.1007/s10958-017-3337-0
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… read more here.
Keywords: integer solutions; equations quadratic; matrix linear; solutions matrix ... See more keywords
On the magnitude of the integer solutions of the semi-diagonal equation ax2 + by2 + cz2 + dxy = 0
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DOI: 10.1142/s1793042119500040
Abstract: In this paper, I generalize Holzer’s theorem for semi-diagonal equation. read more here.
Keywords: integer solutions; diagonal equation; solutions semi; semi diagonal ... See more keywords
Nonnegative integer solutions of the equationFn
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DOI: 10.3906/mat-1810-83
Abstract: In this study, we solve the Diophantine equation in the title in nonnegative integers $m,n,$ and $a$. The solutions are given by $F_{1}-F_{0}=F_{2}-F_{0}=F_{3}-F_{2}=F_{3}-F_{1}=F_{4}-F_{3}=5^{0}$ and $F_{5}-F_{0}=F_{6}-F_{4}=F_{7}-F_{6}=5.$ Then we give a conjecture that says that if $a\geq… read more here.
Keywords: integer solutions; nonnegative integer; solutions equationfn;