Bounds on positive integral solutions of linear Diophantine equations
Bounds on positive integral solutions of linear Diophantine equations
Assuming the existence of a solution, we find bounds for small solutions <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x"> <mml:semantics> <mml:mi>x</mml:mi> <mml:annotation encoding="application/x-tex">x</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the finite matrix equation <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A x equals upper B"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:mi>B</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">Ax = B</mml:annotation> …