A sharp bound for solutions of linear Diophantine equations
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Let Ax = b be an m n system of linear equations with rank m and integer coefficients. Denote by Y the maximum of the absolute values of the m m minors of the augmented matrix (A, b). It is proved that if the system has an integral solution, then it has an integral solution x = (xi) with max xi Y. The bound is sharp. 1989 American Mathematical Society.