explain With the above notation, consider the equation c = car + cbs. Since a divides c, ab must divide cbs (since b is relatively prime to a and hence does not divide a). Similarly, since b divides c, ab must divide car. Thus, ab divides c. This is a direct application of the definition of divisibility: if ab divides car and cbs, then there exists an integer k such that car = abk and cbs = abk, which implies that c = ab(kr + ks), showing that ab divides c. This completes the proof