In the Rambam's Mishne Tora, the end of chapter 8 of M'lachim reads:
Any [gentile] who accepts seven commands and is careful to fulfill them is among the pious of the nations of the world and has a share in the world to come. But that's provided he accepts them and does them because God commanded them in the Torah and informed us through our leader Moshe that descendants of Noach had been commanded them. If, on the other hand, he does them because of the force of logic, he is… not one of the pious of the nations of the world, but one of their wise men.
Now, Jews must — again, I'll quote Mishne Tora, this time from Y'sode Hatora chapter 1:
know there is a first existing thing who brings all that exists into existence.…
And if one could conceive that all other things in existence, except him, would not exist, then he alone would exist: he would not be nonexistent due to their nonexistence, for all existing things require him but he does not require them or any one of them. Thus, his truth is not the truth of any one of them:… there is no truly existing thing besides him like him.…
And he guides the wheel with infinite strength, with unending strength….
And this god is… not one like a type that includes many individuals, and not one like a body that has many divisions and extents, but a oneness like no other.…
It's clear in the Torah and the books of the prophets that God is no body….
We seem to have a few aspects of God that Rambam holds necessary for Jews to believe (or know): that he exists, that he creates every other existence, that his existence is true whereas others' is dependent on his, that he guides all events, that he is indivisible, and that he is incorporeal.
Which of these beliefs, according to Rambam, are required of gentiles in order to be considered "among the pious of the nations of the world and [to have] a share in the world to come"?