Suppose that the positive integer n has the property that is divisible by 3.

if , where and are distinct odd primes with , then p = 3 and ).

if then

working modulo 3, p can take any of the values 0, 1, 2 but q can take only values 1 or 2 since is prime.

Now, I can understand why p can only take values 0, 1, 2, but why can q only take values 1 or 2? q > 3 is prime? I don't understand what is meant by this. Obviously and is not prime for all q, and if q is defined as a odd prime this is just a pointless statement, so what does it mean and why does it put restrictions on what values q can take modulo 3?