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.
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