Prove: the sum of four consecutive integers is never divisible by 4 g

Yup, that's right. Your integers are n, n+1, n+2, n+3. You add them up to get 4n+6. If you don't want to talk about remainders or congreuences, then you can also say that 4n+64=n+64=n+1+12. And ...

Missing: g