Give an example of three positive integers m, n, and r, and three integers a, b, and c such that the gcd of m, n, and r is 1, but there is no simultaneous solution to x ≡ a (mod m) x ≡ b (mod n) x ≡ c (mod r). remark: this is to highlight the necessity of "relatively prime" in the hypothesis of the chinese remainder theorem.