Consider:

int sum(const int numbers[], const int size){
    if (size == 0)
        return 0;
    else
        return numbers[0] + sum(numbers+1, size-1);
}

This is a simple recursive function from MIT 6.096 for adding an arbitrary number of integers, and it works.

The thing I cannot understand is in the last line:

How does numbers+1 work, given numbers[] is an int array and you shouldn't be able to add an integer to an int[] constant?

how does "numbers+1" work, given numbers[] is an int array and you shouldn't be able to add an integer to an int[] constant?

There's no int[] constant. numbers is decayed to a pointer and numbers+1 is simple pointer arithmetic applied to the parameter passed to the recursive call.