Small solutions of linear Diophantine equations

A Sharp Bound for Solutions of Linear Diophantine Equations

“…In [3] the conjecture was made that for the second type of problems a nonnegative integral solutions exists with components bounded by the pxp minors of the augmented matrix, where p is the rank of the matrix. This conjecture was proved in several special cases and weaker results were proved in the general case in [4,5]; however, it is still open in the general case.…”

“…The existence of small integral solutions to systems of linear equations with integral coefficients has been discussed previously in [1,2,3,4,5,6,7,8,11]. Two types of problems have been considered.…”

“…Gomory [10] has shown that if (4) has an integer solution, then it has a nonnegative integer solution with (5) Xm+\ + Xm+2 + + *< |*|-1.…”

A sharp bound for solutions of linear Diophantine equations

“…In [3] the conjecture was made that for the second type of problems a nonnegative integral solutions exists with components bounded by the pxp minors of the augmented matrix, where p is the rank of the matrix. This conjecture was proved in several special cases and weaker results were proved in the general case in [4,5]; however, it is still open in the general case.…”

“…The existence of small integral solutions to systems of linear equations with integral coefficients has been discussed previously in [1,2,3,4,5,6,7,8,11]. Two types of problems have been considered.…”