ABSTRACT The modular n-queen problem in higher dimensions was introduced by Nudelman . He showed that for a complete solution to exist in the d-dimensional modular n-chessboard, it is necessary that gcd(n, (2d 1)!) = 1, and that it is su#cient that gcd(n, (2 1)!) = 1. He conjectured that the last condition is also necessary and showed that this is indeed the case for the class of linear solutions. In this notes, we observe that the conjecture is true for the larger class of polynomial solutions, which are solutions we present as a natural generalization of the bidimensional solutions developed by Klove . We also generalize constructions of bidimensional solutions developed also by Klove .