Question

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

Answer 1

$n+n+1+n+2+n+3=4n+6$

4n is divisible by 4, but 6 is not, so the sum 4n+6 is not divisble by 4.

Answer 2

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