- In this question \(p\) and \(q\) are positive integers with \(q > p\)
Statement 1: \(q ^ { 3 } - p ^ { 3 }\) is never a multiple of 5
- Show, by means of a counter example, that Statement 1 is not true.
Statement 2: When \(p\) and \(q\) are consecutive even integers \(q ^ { 3 } - p ^ { 3 }\) is a multiple of 8
- Prove, using algebra, that Statement 2 is true.