Theorem 3, primes q = 3 mod 4 below 400 (q, form, all checks pass): [(3, 'I', True), (7, 'I', True), (11, 'II', True), (19, 'I', True), (23, 'II', True), (31, 'I', True), (43, 'I', True), (47, 'II', True), (59, 'II', True), (67, 'I', True), (71, 'II', True), (79, 'I', True), (83, 'II', True), (103, 'I', True), (107, 'II', True), (127, 'I', True), (131, 'II', True), (139, 'I', True), (151, 'I', True), (163, 'I', True), (167, 'II', True), (179, 'II', True), (191, 'II', True), (199, 'I', True), (211, 'I', True), (223, 'I', True), (227, 'II', True), (239, 'II', True), (251, 'II', True), (263, 'II', True), (271, 'I', True), (283, 'I', True), (307, 'I', True), (311, 'II', True), (331, 'I', True), (347, 'II', True), (359, 'II', True), (367, 'I', True), (379, 'I', True), (383, 'II', True)]
all pass: True count 40
Theorem 4, 60 random admissible (d,A,B,k): all pass: True
