论文信息 - Small solutions of linear Diophantine equations

Small solutions of linear Diophantine equations

Abstract Let Ax = B be a system of m × n linear equations with integer coefficients. Assume the rows of A are linearly independent and denote by X (respectively Y ) the maximum of the absolute values of the m × m minors of the matrix A (the augmented matrix ( A , B )). If the system has a solution in nonnegative integers, it is proved that the system has a solution X = ( x i ) in nonnegative integers wity x i ⩽ X for n - m variables and x i ⩽ ( m - m + 1) Y for m variables. This improves previous results of the authors and others.

I. Borosh | M. Flahive | B. Treybig

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