A note on Fox colorings of virtual tangles

We study Fox colorings of tangle diagrams by [Formula: see text] or [Formula: see text], where [Formula: see text] is odd. For an [Formula: see text]-colored [Formula: see text]-string tangle diagram, the colors at the [Formula: see text] boundary points form a vector [Formula: see text]. We show that a vector [Formula: see text] arises from an [Formula: see text]-colored classical tangle diagram if and only if the alternating sum [Formula: see text] vanishes. We then determine how this restriction changes for virtual tangle diagrams. For [Formula: see text], the realizability of a vector [Formula: see text] is characterized by a divisibility condition on [Formula: see text]. For [Formula: see text], every vector [Formula: see text] is realizable by a virtual tangle diagram.