3. (i) Show that the following statement is false: $$\text { " } ( n + 1 ) ^ { 3 } - n ^ { 3 } \text { is prime for all } n \in \mathbb { N } \text { " }$$ (ii) Given that the points \(A ( 1,0 ) , B ( 3 , - 10 )\) and \(C ( 7 , - 6 )\) lie on a circle, prove that \(A B\) is a diameter of this circle.