 In general, a linear Diophantine equation has no solutions, or an infinite number of solutions.To find the latter, consider two solutions, ("x"1, "y"1) and ("x"2, "y"2), where

or equivalently

Therefore, the smallest difference between two "x" solutions is "b"/"g", whereas the smallest difference between two "y" solutions is "a"/"g".Thus, the solutions may be expressed as

By allowing "u" to vary over all possible integers, an infinite family of solutions can be generated from a single solution ("x"1, "y"1).