Can const member function return a non-const pointer to a data member?

Code goes first:

class A
{
    public:
        ...
        int *foo() const
        {
            return _px;
        }
    private:
        int *_px;
}

The member function foo returns a non-const pointer to private member _px, which, I think, opens a door to modifying member _px, right?

Is foo a const member function? Should I add a const in front of the return type?

UPDATE

What a const-member-function should guarantee is that, it cannot change any data-member, right?

In my case, function foo doesn't open a door to modifying class As data-member _px, but a door to modifying what _px pointing to, So my question is, does this violate what a const-function should guarantee?

A const member function can only return a const pointer or reference to a member.

However, your example isn't returning a pointer to a member; it's returning a copy of a member that happens to be a pointer. That is allowed in a const member function (even if the pointer happens to point to another member).

This would not be allowed (note that it's now returning a reference):

int *& foo() const {return _px;}

but this would (returning a const reference):

int * const & foo() const {return _px;}