Analysis of Quadratic Residue over Z₁₂₅

Quadratic residue (QR)	x such that x2 = QR mod 125	Occurance
0	0, 25, 50, 75, 100	5
1	1, 124	2
4	2, 123	2
6	16, 109	2
9	3, 122	2
11	56, 69	2
14	42, 83	2
16	4, 121	2
19	12, 113	2
21	39, 86	2
24	32, 93	2
25	5, 20, 30, 45, 55, 70, 80, 95, 105, 120	10
26	49, 76	2
29	23, 102	2
31	34, 91	2
34	28, 97	2
36	6, 119	2
39	17, 108	2
41	54, 71	2
44	13, 112	2
46	36, 89	2
49	7, 118	2
51	26, 99	2
54	48, 77	2
56	41, 84	2
59	53, 72	2
61	44, 81	2
64	8, 117	2
66	21, 104	2
69	38, 87	2
71	14, 111	2
74	18, 107	2
76	24, 101	2
79	52, 73	2
81	9, 116	2
84	47, 78	2
86	31, 94	2
89	33, 92	2
91	29, 96	2
94	62, 63	2
96	61, 64	2
99	43, 82	2
100	10, 15, 35, 40, 60, 65, 85, 90, 110, 115	10
101	51, 74	2
104	27, 98	2
106	59, 66	2
109	22, 103	2
111	19, 106	2
114	58, 67	2
116	46, 79	2
119	37, 88	2
121	11, 114	2
124	57, 68	2

Occurance	Quadratic residues	Total QRs with same occurance
2	1, 4, 6, 9, 11, 14, 16, 19, 21, 24, 26, 29, 31, 34, 36, 39, 41, 44, 46, 49, 51, 54, 56, 59, 61, 64, 66, 69, 71, 74, 76, 79, 81, 84, 86, 89, 91, 94, 96, 99, 101, 104, 106, 109, 111, 114, 116, 119, 121, 124	50
5	0	1
10	25, 100	2