Suppose that gcd(a,b)=1 and suppose further that a divides the product bc. Show that a must divide c. -------------------------------------------------------------------------- Please I need a detailed proof, Thanks! Solution Since gcd(a,b) = 1, by the Euclidean Algorithm, we know that it is possible to have the equation ax + by = 1 where x and y are both integers. If we multiply this through by c, we get that acx + bcy = c. Since a|acx, and since a|bc implies that a|bcy, we know that a|(acx+bcy), or equivalently, a|c..