before you go there - you need to be sure of a few things (so that you know what are you proving and what are you using to generate your proofs)
1. What is the definition of "set of integers"? What are the properties/axioms of this set (for e.g. induciton)?
2. How do you define '+'? What are the properties/axioms on '+'?
3. How do you define '.'? What are the properties/axioms on '.'?
If you have not thought about these, I would suggest you spend a little time in getting a grasp of the above first and then attempt your problem