On the points on the unit circle with finite b-adic expansions

Let b > 1 be an arbitrary integer base and let 1 greater than or equal to 0 be the number of different prime factors p(j) of b with p(j) equivalent to 1 mod 4, j = 1,..., l. Further let Pi(b) be the set of points on the unit circle with finite b-adic expansions of their coordinates and let Phi(b) be the set of angles of the points P epsilon Pi(b). Then Phi(b) is an additiv e group which is the direct sum of 1 infinite cyclic groups and of the fini te cyclic group (pi/2). If in case of 1 > 0 the points of nb are arranged a ccording to the number of digits of their coordinates, their the arising se quence P-0, P-1,... is uniformly distributed on the unit circle. On the oth er hand, in case of l = 0 the only points in Pi(b) are the exceptional poin ts (1, 0), (0, 1), (-1, 0), (0, -1). The proofs are based on a canonical fo rm for all integer solutions x, y of x(2) + y(2) = b(2k).