7 It is given that any integer can be expressed in the form \(3 m + r\), where \(m\) is an integer and \(r\) is 0,1 or 2 .
Use this fact to answer the following.
- By considering the different values of \(r\), prove that the square of any integer cannot be expressed in the form \(3 n + 2\), where \(n\) is an integer.
- Three integers are chosen at random from the integers 1 to 99 inclusive. The three integers are not necessarily different.
By considering the different values of \(r\), determine the probability that the sum of these three integers is divisible by 3 .