What is a linear Diophantine Equation? The simplest linear Diophantine equation takes the form ax + by = d , where a , b and c are given integers. The solutions are described by the following theorem: This Diophantine equation has a solution (where x and y are integers) if and only if c is a multiple of the greatest common divisor of a and b . Moreover, if ( x , y ) is a solution, then the other solutions have the form ( x + kv , y − ku ) , where k is an arbitrary integer, and u and v are the quotients of a and b (respectively) by the greatest common divisor of a and b . (source: wiki) To know whether a linear diophantine equation has integer solutions, we...
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