the system has a unique + oy 3. If ad- bc #0, then for every r, S cx + dy = S solution (x, y). An explicit formula for x, y shows: a, b, c, d, r, s, € Z implies x, y ≤ qq. What conditions on a, b, c, d guarantee that the solution x, y will always be integers? Interpret this as a statement about vectors (a, b) and w = (c, d), and the lattice of all linear combinations xv + yw for x, y ≤ Z. How does this generalize to systems of 3 equations in 3 unknowns? -

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