A Sharp Bound for Solutions of Linear Diophantine Equations

DOI10.2307/2047041zbMath0672.15006OpenAlexW4242691767MaRDI QIDQ3825192

David S. Rubin, Bruce Treybig, Mary E. Flahive, Itshak Borosh

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2047041

zbMATH Keywords

ranklinear Diophantine equationsboundminorsintegral solution

Mathematics Subject Classification ID

Integer programming (90C10) Linear Diophantine equations (11D04) Matrices of integers (15B36) Linear equations (linear algebraic aspects) (15A06)

Related Items (12)

Satisfiability with index dependency ⋮ Nonnegative elements of subgroups of \(\mathbb{Z}^ n\) ⋮ Effective Results for Discriminant Equations over Finitely Generated Integral Domains ⋮ Counting basis extensions in a lattice ⋮ A note on Hamiltonian cycles in planar graphs ⋮ New bounds in reduction theory of indefinite ternary integral quadratic forms ⋮ Representing integers by multilinear polynomials ⋮ Two conjectures on the arithmetic in ℝ and ℂ ⋮ Effective results for points on certain subvarieties of tori ⋮ Higher mathematics with the beam scale ⋮ Exponents of tuples of nonnegative matrices ⋮ Exponents of nonnegative matrix pairs

Cites Work

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• On Siegel's lemma
• Small solutions of linear diophantine equations
• Some polyhedra related to combinatorial problems
• Bounds on Positive Integral Solutions of Linear Diophantine Equations II
• On the complexity of integer programming
• Bounds on Positive Integral Solutions of Linear Diophantine Equations
• A Sharp Bound for Positive Solutions of Homogeneous Linear Diophantine Equations
• A Bound on Solutions of Linear Integer Equalities and Inequalities

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