and cannot be both odd, otherwise would all be even. Hence one of and must be even. Hence is always divisible by 4.
If one of and is divisible by 3, then would also be divisible by 3. Suppose neither nor is a multiple of 3. Then 3 does not divide or either. Now, either or In the former case, is divisible by 3. In the latter case, we have and 3 divides
If one of and is divisible by 5, then would also be divisible by 5. Suppose 5 does not divide or By Fermat’s little theorem, and Hence 5 divides As 5 is prime, this means 5 divides either or