Prove these 4 theorems:

1. Prove that if a and b are even then a^2+b is even

2. Prove if a is even, and b is an integer, then ab is even.

3. Prove if a is even and b is odd then a^2+b^2 is odd

4. Prove if a and b are divisible by 3, and u and v are integers, then au+bv is divisible by 3.