let a,b, and c be integers such that if (a,c)=1 and (b,c)=1, then prove that (ab,c)=1

Consider the following proof that if x and y are two even integers, then their sum is even. Proof: Assume that x and y are two even integers but their sum is not even, then x + y is odd. By definition, there are some integers p, q, and k such that x = 2p, y = 2q, and x + y = 2k + 1. Therefore, 2k + 1 = x + y = 2p + 2q. Rewrite above equation, we have 2(p + q - k) = 1, which is impossible. Which proof method is used in above proof. O Proof by counterexample Direct proof Proof by contraposition O Proof by contradiction

Use the method of proof by contradiction to prove that their exist no integers a and b for when 18a + 6b = 1

prove For all integers a, b, c, and d, if a|c and b|d then ab|cd.