Nemeth Tests from the PreTeXt/NFB project on Judson's Aata.

Nemeth Tests from the PreTeXt/NFB project on Judson's Aata. Locale: nemeth, Style: Verbose.

0	$r \equiv s (\mod n)$	⠗⠀⠸⠇⠀⠎⠷⠍⠕⠙⠀⠝⠾
1	$y = x^{E} \mod n$	⠽⠀⠨⠅⠀⠭⠘⠠⠑⠐⠍⠕⠙⠀⠝
2	$\| \tilde{X} \| = 2^{4} = 16$	⠳⠐⠠⠭⠣⠈⠱⠻⠳⠀⠨⠅⠀⠼⠆⠘⠲⠀⠨⠅⠀⠼⠂⠖
3	$S$	⠈⠰⠠⠎
4	$a x^{2} + b x + c = 0$	⠁⠭⠘⠆⠐⠬⠃⠭⠬⠉⠀⠨⠅⠀⠼⠴
5	$A \overset{f}{\to} B$	⠠⠁⠀⠐⠫⠒⠒⠕⠣⠋⠻⠀⠠⠃
6	$g (x) = \sqrt[3]{x}$	⠛⠷⠭⠾⠀⠨⠅⠀⠣⠒⠜⠭⠻
7	$T_{A}^{- 1} = T_{A^{- 1}}$	⠠⠞⠰⠠⠁⠘⠤⠂⠀⠨⠅⠀⠠⠞⠰⠠⠁⠰⠘⠤⠂
8	$⋃_{k} X_{k} = X$	⠐⠨⠬⠩⠅⠻⠠⠭⠰⠅⠀⠨⠅⠀⠠⠭
9	$f (p / q) = \frac{p + 1}{p - 2}$	⠋⠷⠏⠸⠌⠟⠾⠀⠨⠅⠀⠹⠏⠬⠂⠌⠏⠤⠆⠼
10	$X = N \cup {\sqrt{2}}$	⠠⠭⠀⠨⠅⠀⠈⠰⠠⠝⠨⠬⠨⠷⠜⠆⠻⠨⠾
11	$\bar{z} = a - b i$	⠵⠱⠀⠨⠅⠀⠁⠤⠃⠊
12	$Z_{8}$	⠈⠰⠠⠵⠦
13	$C = {y : G x = y for x \in Z_{2}^{k}}$	⠠⠉⠀⠨⠅⠀⠨⠷⠸⠰⠽⠸⠒⠠⠛⠸⠰⠭⠀⠨⠅⠀⠸⠰⠽⠋⠕⠗⠸⠰⠭⠀⠈⠑⠀⠈⠰⠠⠵⠆⠘⠅⠐⠨⠾
14	$\sqrt{2 + \sqrt{3}}$	⠜⠆⠬⠨⠜⠒⠨⠻⠻
15	$\sqrt{\sqrt[3]{2} - i}$	⠜⠨⠣⠒⠜⠆⠨⠻⠤⠊⠻
16	$R^{3}$	⠈⠰⠠⠗⠘⠒
17	${\tilde{X}}_{(1)} = \tilde{X}$	⠐⠠⠭⠣⠈⠱⠻⠰⠷⠂⠾⠀⠨⠅⠀⠐⠠⠭⠣⠈⠱⠻
18	$G_{0} = {A : (A, b) \in G for some b}$	⠠⠛⠴⠀⠨⠅⠀⠨⠷⠠⠁⠸⠒⠷⠠⠁⠠⠀⠃⠾⠀⠈⠑⠀⠠⠛⠋⠕⠗⠀⠎⠕⠍⠑⠃⠨⠾
19	$300!$	⠼⠒⠴⠴⠯
20	$A \cup (B \cup C) = (A \cup B) \cup C$	⠠⠁⠨⠬⠷⠠⠃⠨⠬⠠⠉⠾⠀⠨⠅⠀⠷⠠⠁⠨⠬⠠⠃⠾⠨⠬⠠⠉
21	$(\binom{n}{k})$	⠠⠷⠝⠠⠾⠀⠠⠷⠅⠠⠾
22	$3 + 56 - 13 + 8 / 2$	⠼⠒⠬⠢⠖⠤⠂⠒⠬⠦⠸⠌⠆
23	$w (x) = d (x, 0)$	⠺⠷⠸⠰⠭⠾⠀⠨⠅⠀⠙⠷⠸⠰⠭⠠⠀⠸⠼⠴⠾
24	$6.00000 + 0.00000 i$	⠼⠖⠨⠴⠴⠴⠴⠴⠬⠴⠨⠴⠴⠴⠴⠴⠊
25	$p = 0.0001$	⠏⠀⠨⠅⠀⠼⠴⠨⠴⠴⠴⠂
26	$p = 0.01$	⠏⠀⠨⠅⠀⠼⠴⠨⠴⠂
27	$p = 0.995$	⠏⠀⠨⠅⠀⠼⠴⠨⠔⠔⠢
28	$p = 0.999$	⠏⠀⠨⠅⠀⠼⠴⠨⠔⠔⠔
29	$A = 00, B = 01, \dots, Z = 25$	⠠⠁⠀⠨⠅⠀⠼⠴⠴⠠⠀⠠⠃⠀⠨⠅⠀⠼⠴⠂⠠⠀⠄⠄⠄⠠⠀⠠⠵⠀⠨⠅⠀⠼⠆⠢
30	$(000)$	⠷⠴⠴⠴⠾
31	$0000$	⠼⠴⠴⠴⠴
32	$c_{1} = (00000)$	⠸⠰⠉⠂⠀⠨⠅⠀⠷⠴⠴⠴⠴⠴⠾
33	$(00001) + C$	⠷⠴⠴⠴⠴⠂⠾⠬⠠⠉
34	$(0000101100)$	⠷⠴⠴⠴⠴⠂⠴⠂⠂⠴⠴⠾
35	$(00010) + C$	⠷⠴⠴⠴⠂⠴⠾⠬⠠⠉
36	$z = (00011)$	⠸⠰⠵⠀⠨⠅⠀⠷⠴⠴⠴⠂⠂⠾
37	$001$	⠼⠴⠴⠂
38	$(00100) + C$	⠷⠴⠴⠂⠴⠴⠾⠬⠠⠉
39	$(0010000101)$	⠷⠴⠴⠂⠴⠴⠴⠴⠂⠴⠂⠾
40	$(001001)$	⠷⠴⠴⠂⠴⠴⠂⠾
41	$(01000) (00101) (11011) (10110)$	⠷⠴⠂⠴⠴⠴⠾⠷⠴⠴⠂⠴⠂⠾⠷⠂⠂⠴⠂⠂⠾⠷⠂⠴⠂⠂⠴⠾
42	$0011$	⠼⠴⠴⠂⠂
43	$(00110) + C$	⠷⠴⠴⠂⠂⠴⠾⠬⠠⠉
44	$c_{2} = (00111)$	⠸⠰⠉⠆⠀⠨⠅⠀⠷⠴⠴⠂⠂⠂⠾
45	$010$	⠼⠴⠂⠴
46	$(0100 0101)$	⠷⠼⠴⠂⠴⠴⠀⠼⠴⠂⠴⠂⠾
47	$(01000) + C$	⠷⠴⠂⠴⠴⠴⠾⠬⠠⠉
48	$(00100) (01001) (10111) (11010)$	⠷⠴⠴⠂⠴⠴⠾⠷⠴⠂⠴⠴⠂⠾⠷⠂⠴⠂⠂⠂⠾⠷⠂⠂⠴⠂⠴⠾
49	$x = (010011)^{t}$	⠸⠰⠭⠀⠨⠅⠀⠷⠴⠂⠴⠴⠂⠂⠾⠘⠞
50	$(00111) (01010) (10100) (11001)$	⠷⠴⠴⠂⠂⠂⠾⠷⠴⠂⠴⠂⠴⠾⠷⠂⠴⠂⠴⠴⠾⠷⠂⠂⠴⠴⠂⠾
51	$(011100) (011011) (111011) (100011) (000000) (010101) (110100) (110011)$	⠷⠴⠂⠂⠂⠴⠴⠾⠷⠴⠂⠂⠴⠂⠂⠾⠷⠂⠂⠂⠴⠂⠂⠾⠷⠂⠴⠴⠴⠂⠂⠾⠷⠴⠴⠴⠴⠴⠴⠾⠷⠴⠂⠴⠂⠴⠂⠾⠷⠂⠂⠴⠂⠴⠴⠾⠷⠂⠂⠴⠴⠂⠂⠾
52	$(11110101), (01010100)$	⠷⠂⠂⠂⠂⠴⠂⠴⠂⠾⠠⠀⠷⠴⠂⠴⠂⠴⠂⠴⠴⠾
53	$z = (010111)^{t}$	⠸⠰⠵⠀⠨⠅⠀⠷⠴⠂⠴⠂⠂⠂⠾⠘⠞
54	$011$	⠼⠴⠂⠂
55	$(0110)$	⠷⠴⠂⠂⠴⠾
56	$(00001) (01100) (10010) (11111)$	⠷⠴⠴⠴⠴⠂⠾⠷⠴⠂⠂⠴⠴⠾⠷⠂⠴⠴⠂⠴⠾⠷⠂⠂⠂⠂⠂⠾
57	$x = (011001)^{t}$	⠸⠰⠭⠀⠨⠅⠀⠷⠴⠂⠂⠴⠴⠂⠾⠘⠞
58	$(011010), (011100)$	⠷⠴⠂⠂⠴⠂⠴⠾⠠⠀⠷⠴⠂⠂⠂⠴⠴⠾
59	$(0110110) (0111100) (1110000) (1111111) (1001001) (1000011) (0001111) (0000000)$	⠷⠴⠂⠂⠴⠂⠂⠴⠾⠷⠴⠂⠂⠂⠂⠴⠴⠾⠷⠂⠂⠂⠴⠴⠴⠴⠾⠷⠂⠂⠂⠂⠂⠂⠂⠾⠷⠂⠴⠴⠂⠴⠴⠂⠾⠷⠂⠴⠴⠴⠴⠂⠂⠾⠷⠴⠴⠴⠂⠂⠂⠂⠾⠷⠴⠴⠴⠴⠴⠴⠴⠾
60	$(1001), (0111)$	⠷⠂⠴⠴⠂⠾⠠⠀⠷⠴⠂⠂⠂⠾
61	$(10000) (11101) (00011) (01110)$	⠷⠂⠴⠴⠴⠴⠾⠷⠂⠂⠂⠴⠂⠾⠷⠴⠴⠴⠂⠂⠾⠷⠴⠂⠂⠂⠴⠾
62	$(00010) (01111) (10001) (11100)$	⠷⠴⠴⠴⠂⠴⠾⠷⠴⠂⠂⠂⠂⠾⠷⠂⠴⠴⠴⠂⠾⠷⠂⠂⠂⠴⠴⠾
63	$A = 00, B = 02, \dots, Z = 25$	⠠⠁⠀⠨⠅⠀⠼⠴⠴⠠⠀⠠⠃⠀⠨⠅⠀⠼⠴⠆⠠⠀⠄⠄⠄⠠⠀⠠⠵⠀⠨⠅⠀⠼⠆⠢
64	$c = 4 598 037 234$	⠉⠀⠨⠅⠀⠼⠲⠀⠢⠔⠦⠀⠴⠒⠶⠀⠆⠒⠲
65	$E = 04$	⠠⠑⠀⠨⠅⠀⠼⠴⠲
66	$10 / 5 = 2$	⠼⠂⠴⠸⠌⠢⠀⠨⠅⠀⠼⠆
67	$(1254)^{100}$	⠷⠂⠆⠢⠲⠾⠘⠂⠴⠴
68	$1000$	⠼⠂⠴⠴⠴
69	$(10000) + C$	⠷⠂⠴⠴⠴⠴⠾⠬⠠⠉
70	$(1001 1000)$	⠷⠼⠂⠴⠴⠂⠀⠼⠂⠴⠴⠴⠾
71	$(101)$	⠷⠂⠴⠂⠾
72	$y = (1010)$	⠸⠰⠽⠀⠨⠅⠀⠷⠂⠴⠂⠴⠾
73	$(10100) + C$	⠷⠂⠴⠂⠴⠴⠾⠬⠠⠉
74	$x = (10101)$	⠸⠰⠭⠀⠨⠅⠀⠷⠂⠴⠂⠴⠂⠾
75	$(101011)$	⠷⠂⠴⠂⠴⠂⠂⠾
76	$(1011)$	⠷⠂⠴⠂⠂⠾
77	$(000000), (010111), (101101), (111010)$	⠷⠴⠴⠴⠴⠴⠴⠾⠠⠀⠷⠴⠂⠴⠂⠂⠂⠾⠠⠀⠷⠂⠴⠂⠂⠴⠂⠾⠠⠀⠷⠂⠂⠂⠴⠂⠴⠾
78	$gcd (120, 102) = 6$	⠛⠉⠙⠀⠷⠂⠆⠴⠠⠀⠂⠴⠆⠾⠀⠨⠅⠀⠼⠖
79	$108$	⠼⠂⠴⠦
80	$110$	⠼⠂⠂⠴
81	$y = (1100)$	⠸⠰⠽⠀⠨⠅⠀⠷⠂⠂⠴⠴⠾
82	$(00110) (01011) (10101) (11000)$	⠷⠴⠴⠂⠂⠴⠾⠷⠴⠂⠴⠂⠂⠾⠷⠂⠴⠂⠴⠂⠾⠷⠂⠂⠴⠴⠴⠾
83	$(011010) (011100) (110111) (110000)$	⠷⠴⠂⠂⠴⠂⠴⠾⠷⠴⠂⠂⠂⠴⠴⠾⠷⠂⠂⠴⠂⠂⠂⠾⠷⠂⠂⠴⠴⠴⠴⠾
84	$(000000) (011100) (110101) (110001)$	⠷⠴⠴⠴⠴⠴⠴⠾⠷⠴⠂⠂⠂⠴⠴⠾⠷⠂⠂⠴⠂⠴⠂⠾⠷⠂⠂⠴⠴⠴⠂⠾
85	$x = (1101)$	⠸⠰⠭⠀⠨⠅⠀⠷⠂⠂⠴⠂⠾
86	$y = (11010)$	⠸⠰⠽⠀⠨⠅⠀⠷⠂⠂⠴⠂⠴⠾
87	$y = (110101)^{t}$	⠸⠰⠽⠀⠨⠅⠀⠷⠂⠂⠴⠂⠴⠂⠾⠘⠞
88	$c_{4} = (11011)$	⠸⠰⠉⠲⠀⠨⠅⠀⠷⠂⠂⠴⠂⠂⠾
89	$(110110)$	⠷⠂⠂⠴⠂⠂⠴⠾
90	$(111)$	⠷⠂⠂⠂⠾
91	$(0110 1110 0110)$	⠷⠼⠴⠂⠂⠴⠀⠼⠂⠂⠂⠴⠀⠼⠴⠂⠂⠴⠾
92	$c_{3} = (11100)$	⠸⠰⠉⠒⠀⠨⠅⠀⠷⠂⠂⠂⠴⠴⠾
93	$1111$	⠼⠂⠂⠂⠂
94	$x = (111110)^{t}$	⠸⠰⠭⠀⠨⠅⠀⠷⠂⠂⠂⠂⠂⠴⠾⠘⠞
95	$y = (111111)^{t}$	⠸⠰⠽⠀⠨⠅⠀⠷⠂⠂⠂⠂⠂⠂⠾⠘⠞
96	$11213525032442$	⠼⠂⠂⠆⠂⠒⠢⠆⠢⠴⠒⠆⠲⠲⠆
97	$7^{6} = 117 649$	⠼⠶⠘⠖⠀⠨⠅⠀⠼⠂⠂⠶⠀⠖⠲⠔
98	$gcd (24, 36) = 12$	⠛⠉⠙⠀⠷⠆⠲⠠⠀⠒⠖⠾⠀⠨⠅⠀⠼⠂⠆
99	$n = 120979, E = 13251, x = 142371$	⠝⠀⠨⠅⠀⠼⠂⠆⠴⠔⠶⠔⠠⠀⠠⠑⠀⠨⠅⠀⠼⠂⠒⠆⠢⠂⠠⠀⠭⠀⠨⠅⠀⠼⠂⠲⠆⠒⠶⠂
100	$(12345) (678)$	⠷⠂⠆⠒⠲⠢⠾⠷⠖⠶⠦⠾
101	$[(1235) (467)]^{- 1}$	⠈⠷⠷⠂⠆⠒⠢⠾⠷⠲⠖⠶⠾⠈⠾⠘⠤⠂
102	$(n, E) = (37986733, 12371)$	⠷⠝⠠⠀⠠⠑⠾⠀⠨⠅⠀⠷⠒⠶⠔⠦⠖⠶⠒⠒⠠⠀⠂⠆⠒⠶⠂⠾
103	$(12453)$	⠷⠂⠆⠲⠢⠒⠾
104	$(12) (1253)$	⠷⠂⠆⠾⠷⠂⠆⠢⠒⠾
105	$(12537)^{- 1}$	⠷⠂⠆⠢⠒⠶⠾⠘⠤⠂
106	$(1254) (13) (25)$	⠷⠂⠆⠢⠲⠾⠷⠂⠒⠾⠷⠆⠢⠾
107	$1260$	⠼⠂⠆⠖⠴
108	$128^{4} = 268, 435, 456$	⠼⠂⠆⠦⠘⠲⠀⠨⠅⠀⠼⠆⠖⠦⠠⠀⠼⠲⠒⠢⠠⠀⠼⠲⠢⠖
109	$n = 79403, D = 671, y = 129381$	⠝⠀⠨⠅⠀⠼⠶⠔⠲⠴⠒⠠⠀⠠⠙⠀⠨⠅⠀⠼⠖⠶⠂⠠⠀⠽⠀⠨⠅⠀⠼⠂⠆⠔⠒⠦⠂
110	$(1423) (34) (56) (1324)$	⠷⠂⠲⠆⠒⠾⠷⠒⠲⠾⠷⠢⠖⠾⠷⠂⠒⠆⠲⠾
111	${(13), (13) (24), (132), (134), (1324), (1342)}$	⠨⠷⠷⠂⠒⠾⠠⠀⠷⠂⠒⠾⠷⠆⠲⠾⠠⠀⠷⠂⠒⠆⠾⠠⠀⠷⠂⠒⠲⠾⠠⠀⠷⠂⠒⠆⠲⠾⠠⠀⠷⠂⠒⠲⠆⠾⠨⠾
112	$(1345) (234)$	⠷⠂⠒⠲⠢⠾⠷⠆⠒⠲⠾
113	$14$	⠼⠂⠲
114	$x = 142528$	⠭⠀⠨⠅⠀⠼⠂⠲⠆⠢⠆⠦
115	$(1426) (142)$	⠷⠂⠲⠆⠖⠾⠷⠂⠲⠆⠾
116	$(142637)$	⠷⠂⠲⠆⠖⠒⠶⠾
117	$(14356)$	⠷⠂⠲⠒⠢⠖⠾
118	$191 E = 1 + 151 m$	⠼⠂⠔⠂⠠⠑⠀⠨⠅⠀⠼⠂⠬⠂⠢⠂⠍
119	$1523$	⠼⠂⠢⠆⠒
120	$1531$	⠼⠂⠢⠒⠂
121	$(17254) (1423) (154632)$	⠷⠂⠶⠆⠢⠲⠾⠷⠂⠲⠆⠒⠾⠷⠂⠢⠲⠖⠒⠆⠾
122	$(156) (234)$	⠷⠂⠢⠖⠾⠷⠆⠒⠲⠾
123	$s = - 16$	⠎⠀⠨⠅⠀⠤⠼⠂⠖
124	$16$	⠸⠼⠂⠖
125	$160$	⠼⠂⠖⠴
126	$μ = (1634)$	⠨⠍⠀⠨⠅⠀⠷⠂⠖⠒⠲⠾
127	$(n, E) = (16394854313, 34578451)$	⠷⠝⠠⠀⠠⠑⠾⠀⠨⠅⠀⠷⠂⠖⠒⠔⠲⠦⠢⠲⠒⠂⠒⠠⠀⠒⠲⠢⠶⠦⠲⠢⠂⠾
128	$5 \cdot 7 \cdot 47 = 1645$	⠼⠢⠡⠶⠡⠲⠶⠀⠨⠅⠀⠼⠂⠖⠲⠢
129	$165$	⠼⠂⠖⠢
130	$168$	⠼⠂⠖⠦
131	$41 \equiv 17 (\mod 8)$	⠼⠲⠂⠀⠸⠇⠀⠼⠂⠶⠷⠍⠕⠙⠀⠼⠦⠾
132	$(17352)$	⠷⠂⠶⠒⠢⠆⠾
133	$1739$	⠼⠂⠶⠒⠔
134	$175$	⠼⠂⠶⠢
135	$180^{\circ}$	⠼⠂⠦⠴⠘⠨⠡
136	$19$	⠼⠂⠔
137	$(n, E) = (3053, 1921)$	⠷⠝⠠⠀⠠⠑⠾⠀⠨⠅⠀⠷⠒⠴⠢⠒⠠⠀⠂⠔⠆⠂⠾
138	$196,833 \times 196,833$	⠼⠂⠔⠖⠠⠦⠒⠒⠈⠡⠂⠔⠖⠠⠦⠒⠒
139	$19945$	⠼⠂⠔⠔⠲⠢
140	$n = 3551, D = 1997, y = 2791$	⠝⠀⠨⠅⠀⠼⠒⠢⠢⠂⠠⠀⠠⠙⠀⠨⠅⠀⠼⠂⠔⠔⠶⠠⠀⠽⠀⠨⠅⠀⠼⠆⠶⠔⠂
141	$200$	⠼⠆⠴⠴
142	$2000$	⠼⠆⠴⠴⠴
143	$2071^{9521} (\mod 4724)$	⠼⠆⠴⠶⠂⠘⠔⠢⠆⠂⠐⠷⠍⠕⠙⠀⠼⠲⠶⠆⠲⠾
144	$2134$	⠼⠆⠂⠒⠲
145	$x \equiv 214 (\mod 2772)$	⠭⠀⠸⠇⠀⠼⠆⠂⠲⠷⠍⠕⠙⠀⠼⠆⠶⠶⠆⠾
146	$2234 + 4121$	⠼⠆⠆⠒⠲⠬⠲⠂⠆⠂
147	$n = 2257, E = 47, x = 23$	⠝⠀⠨⠅⠀⠼⠆⠆⠢⠶⠠⠀⠠⠑⠀⠨⠅⠀⠼⠲⠶⠠⠀⠭⠀⠨⠅⠀⠼⠆⠒
148	$(n, E) = (451, 231)$	⠷⠝⠠⠀⠠⠑⠾⠀⠨⠅⠀⠷⠲⠢⠂⠠⠀⠆⠒⠂⠾
149	$n = 45629, E = 781, x = 231561$	⠝⠀⠨⠅⠀⠼⠲⠢⠖⠆⠔⠠⠀⠠⠑⠀⠨⠅⠀⠼⠶⠦⠂⠠⠀⠭⠀⠨⠅⠀⠼⠆⠒⠂⠢⠖⠂
150	$234$	⠼⠆⠒⠲
151	$23771$	⠼⠆⠒⠶⠶⠂
152	$41 - 17 = 24$	⠼⠲⠂⠤⠂⠶⠀⠨⠅⠀⠼⠆⠲
153	$72 \in Z_{240}$	⠼⠶⠆⠀⠈⠑⠀⠈⠰⠠⠵⠆⠲⠴
154	$2415$	⠼⠆⠲⠂⠢
155	$N = 250$	⠠⠝⠀⠨⠅⠀⠼⠆⠢⠴
156	$255$	⠼⠆⠢⠢
157	$2557^{341} (\mod 5681)$	⠼⠆⠢⠢⠶⠘⠒⠲⠂⠐⠷⠍⠕⠙⠀⠼⠢⠖⠦⠂⠾
158	$2^{8} = 256$	⠼⠆⠘⠦⠀⠨⠅⠀⠼⠆⠢⠖
159	$5 x + 1 \equiv 13 (\mod 26)$	⠼⠢⠭⠬⠂⠀⠸⠇⠀⠼⠂⠒⠷⠍⠕⠙⠀⠼⠆⠖⠾
160	$2600 = 2^{3} \times 5^{2} \times 13$	⠼⠆⠖⠴⠴⠀⠨⠅⠀⠼⠆⠘⠒⠐⠈⠡⠢⠘⠆⠐⠈⠡⠂⠒
161	$Z_{27}$	⠈⠰⠠⠵⠆⠶
162	$271^{321} (\mod 481)$	⠼⠆⠶⠂⠘⠒⠆⠂⠐⠷⠍⠕⠙⠀⠼⠲⠦⠂⠾
163	$n = 120979, D = 27331, y = 112135$	⠝⠀⠨⠅⠀⠼⠂⠆⠴⠔⠶⠔⠠⠀⠠⠙⠀⠨⠅⠀⠼⠆⠶⠒⠒⠂⠠⠀⠽⠀⠨⠅⠀⠼⠂⠂⠆⠂⠒⠢
164	$2791$	⠼⠆⠶⠔⠂
165	$28$	⠼⠆⠦
166	$q = 29$	⠟⠀⠨⠅⠀⠼⠆⠔
167	$292^{3171} (\mod 582)$	⠼⠆⠔⠆⠘⠒⠂⠶⠂⠐⠷⠍⠕⠙⠀⠼⠢⠦⠆⠾
168	$2134 \cdot 1531 = 3,267,154$	⠼⠆⠂⠒⠲⠡⠂⠢⠒⠂⠀⠨⠅⠀⠼⠒⠠⠆⠖⠶⠠⠂⠢⠲
169	$U (30)$	⠠⠥⠷⠒⠴⠾
170	$n = 3551, E = 629, x = 31$	⠝⠀⠨⠅⠀⠼⠒⠢⠢⠂⠠⠀⠠⠑⠀⠨⠅⠀⠼⠖⠆⠔⠠⠀⠭⠀⠨⠅⠀⠼⠒⠂
171	$312 \in Z_{471}$	⠼⠒⠂⠆⠀⠈⠑⠀⠈⠰⠠⠵⠲⠶⠂
172	$342$	⠼⠒⠲⠆
173	$G = {(1), (12), (345), (354), (12) (345), (12) (354)}$	⠠⠛⠀⠨⠅⠀⠨⠷⠷⠂⠾⠠⠀⠷⠂⠆⠾⠠⠀⠷⠒⠲⠢⠾⠠⠀⠷⠒⠢⠲⠾⠠⠀⠷⠂⠆⠾⠷⠒⠲⠢⠾⠠⠀⠷⠂⠆⠾⠷⠒⠢⠲⠾⠨⠾
174	$44 352 000$	⠼⠲⠲⠀⠒⠢⠆⠀⠴⠴⠴
175	$360^{\circ}$	⠼⠒⠖⠴⠘⠨⠡
176	$37$	⠼⠒⠶
177	$3754$	⠼⠒⠶⠢⠲
178	$38$	⠼⠒⠦
179	$39$	⠼⠒⠔
180	$391 = 17 \cdot 23$	⠼⠒⠔⠂⠀⠨⠅⠀⠼⠂⠶⠡⠆⠒
181	$x = 4$	⠭⠀⠨⠅⠀⠼⠲
182	$40$	⠼⠲⠴
183	$42$	⠼⠲⠆
184	$43 - 18 i$	⠼⠲⠒⠤⠂⠦⠊
185	$n = 8779 \cdot 4327$	⠝⠀⠨⠅⠀⠼⠦⠶⠶⠔⠡⠲⠒⠆⠶
186	$- 4357$	⠤⠼⠲⠒⠢⠶
187	$44$	⠼⠲⠲
188	$46$	⠼⠲⠖
189	$46,388$	⠼⠲⠖⠠⠒⠦⠦
190	$D_{470448}$	⠠⠙⠲⠶⠴⠲⠲⠦
191	$471$	⠼⠲⠶⠂
192	$Z_{48}$	⠈⠰⠠⠵⠲⠦
193	$E = 487$	⠠⠑⠀⠨⠅⠀⠼⠲⠦⠶
194	$U (49)$	⠠⠥⠷⠲⠔⠾
195	$2 + 3 = 5$	⠼⠆⠬⠒⠀⠨⠅⠀⠼⠢
196	$500$	⠼⠢⠴⠴
197	$7! = 5040$	⠼⠶⠯⠀⠀⠨⠅⠀⠼⠢⠴⠲⠴
198	$51$	⠼⠢⠂
199	$2^{511} - 1$	⠼⠆⠘⠢⠂⠂⠐⠤⠂
200	$52$	⠼⠢⠆
201	$53$	⠼⠢⠒
202	$54$	⠼⠢⠲
203	$540 = 2^{2} \cdot 3^{3} \cdot 5$	⠼⠢⠲⠴⠀⠨⠅⠀⠼⠆⠘⠆⠐⠡⠒⠘⠒⠐⠡⠢
204	$561$	⠼⠢⠖⠂
205	$562$	⠼⠢⠖⠆
206	$57 = 2^{0} + 2^{3} + 2^{4} + 2^{5}$	⠼⠢⠶⠀⠨⠅⠀⠼⠆⠘⠴⠐⠬⠆⠘⠒⠐⠬⠆⠘⠲⠐⠬⠆⠘⠢
207	$58$	⠼⠢⠦
208	$n = 5893, D = 81, y = 34$	⠝⠀⠨⠅⠀⠼⠢⠦⠔⠒⠠⠀⠠⠙⠀⠨⠅⠀⠼⠦⠂⠠⠀⠽⠀⠨⠅⠀⠼⠒⠲
209	$59$	⠼⠢⠔
210	$2 x = 6$	⠼⠆⠭⠀⠨⠅⠀⠼⠖
211	$6.00000$	⠼⠖⠨⠴⠴⠴⠴⠴
212	$(1, 2, 4, 8) (3, 6.12, 9) (5, 10) (7, 14, 13, 11)$	⠷⠂⠠⠀⠆⠠⠀⠲⠠⠀⠦⠾⠷⠒⠠⠀⠖⠨⠂⠆⠠⠀⠔⠾⠷⠢⠠⠀⠂⠴⠾⠷⠶⠠⠀⠂⠲⠠⠀⠂⠒⠠⠀⠂⠂⠾
213	$z = 2 cis 60^{\circ}$	⠵⠀⠨⠅⠀⠼⠆⠉⠊⠎⠀⠼⠖⠴⠘⠨⠡
214	$x^{4} - (2 / 3) x^{2} - 62 / 9$	⠭⠘⠲⠐⠤⠷⠆⠸⠌⠒⠾⠭⠘⠆⠐⠤⠖⠆⠸⠌⠔
215	$[GF (625) : GF (25)]$	⠈⠷⠠⠠⠛⠋⠷⠖⠆⠢⠾⠀⠐⠂⠀⠠⠠⠛⠋⠷⠆⠢⠾⠈⠾
216	$631$	⠼⠖⠒⠂
217	$64$	⠼⠖⠲
218	$2^{2^{4}} = 65,536$	⠼⠆⠘⠆⠘⠘⠲⠀⠨⠅⠀⠼⠖⠢⠠⠢⠒⠖
219	$66$	⠼⠖⠖
220	$720$	⠼⠶⠆⠴
221	$729$	⠼⠶⠆⠔
222	$971^{321} (\mod 765)$	⠼⠔⠶⠂⠘⠒⠆⠂⠐⠷⠍⠕⠙⠀⠼⠶⠖⠢⠾
223	$771$	⠼⠶⠶⠂
224	$Z_{10} \times Z_{24} \times Z_{80}$	⠈⠰⠠⠵⠂⠴⠈⠡⠈⠰⠠⠵⠆⠲⠈⠡⠈⠰⠠⠵⠦⠴
225	$7^{5} = 16 807$	⠼⠶⠘⠢⠀⠨⠅⠀⠼⠂⠖⠀⠦⠴⠶
226	$811$	⠼⠦⠂⠂
227	$95 \cdot 97 \cdot 98 \cdot 99 = 89,403,930$	⠼⠔⠢⠡⠔⠶⠡⠔⠦⠡⠔⠔⠀⠨⠅⠀⠼⠦⠔⠠⠲⠴⠒⠠⠔⠒⠴
228	$90^{\circ}$	⠼⠔⠴⠘⠨⠡
229	$945$	⠼⠔⠲⠢
230	$95$	⠼⠔⠢
231	$96$	⠼⠔⠖
232	$97$	⠼⠔⠶
233	$98$	⠼⠔⠦
234	$99$	⠼⠔⠔
235	$9923$	⠼⠔⠔⠆⠒
236	$a \in A$	⠁⠀⠈⠑⠀⠠⠁
237	$Aut (G)$	⠠⠁⠥⠞⠷⠠⠛⠾
238	$A \subset B$	⠠⠁⠀⠸⠐⠅⠀⠠⠃
239	$h : C \to D$	⠓⠸⠒⠀⠠⠉⠀⠫⠕⠀⠠⠙
240	$G \times G \to G$	⠠⠛⠈⠡⠠⠛⠀⠫⠕⠀⠠⠛
241	$GF (p^{n})$	⠠⠠⠛⠋⠷⠏⠘⠝⠐⠾
242	$H = {e}$	⠠⠓⠀⠨⠅⠀⠨⠷⠑⠨⠾
243	$H$	⠈⠰⠠⠓
244	$Hom (V, W)$	⠠⠓⠕⠍⠀⠷⠠⠧⠠⠀⠠⠺⠾
245	$Inn (G)$	⠠⠊⠝⠝⠷⠠⠛⠾
246	$G L_{2} (R)$	⠠⠛⠠⠇⠆⠷⠈⠰⠠⠗⠾
247	$ϕ : L_{H} \to R_{H}$	⠨⠋⠸⠒⠀⠈⠰⠠⠇⠰⠠⠓⠀⠫⠕⠀⠈⠰⠠⠗⠰⠠⠓
248	$M_{2} (R)$	⠈⠰⠠⠍⠆⠷⠈⠰⠠⠗⠾
249	$R / M$	⠠⠗⠸⠌⠠⠍
250	$1 < n < N$	⠼⠂⠀⠐⠅⠀⠝⠀⠐⠅⠀⠠⠝
251	$Null (H)$	⠠⠝⠥⠇⠇⠷⠠⠓⠾
252	$O (n)$	⠠⠕⠷⠝⠾
253	$P A P^{- 1} = B$	⠠⠏⠠⠁⠠⠏⠘⠤⠂⠀⠨⠅⠀⠠⠃
254	$P (R)$	⠈⠰⠠⠏⠷⠈⠰⠠⠗⠾
255	$Q B Q^{- 1} = C$	⠠⠟⠠⠃⠠⠟⠘⠤⠂⠀⠨⠅⠀⠠⠉
256	$R \subset X \times X$	⠠⠗⠀⠸⠐⠅⠀⠠⠭⠈⠡⠠⠭
257	$S = {1, 2, 3}$	⠠⠎⠀⠨⠅⠀⠨⠷⠂⠠⠀⠆⠠⠀⠒⠨⠾
258	$S = 18$	⠠⠎⠀⠨⠅⠀⠼⠂⠦
259	$T_{A} : R^{2} \to R^{2}$	⠠⠞⠰⠠⠁⠸⠒⠀⠈⠰⠠⠗⠘⠆⠀⠫⠕⠀⠈⠰⠠⠗⠘⠆
260	$T = {z \in C^{*} : \| z \| = 1}$	⠈⠰⠠⠞⠀⠨⠅⠀⠨⠷⠵⠀⠈⠑⠀⠈⠰⠠⠉⠘⠈⠼⠸⠒⠳⠵⠳⠀⠨⠅⠀⠼⠂⠨⠾
261	$A \subset U$	⠠⠁⠀⠸⠐⠅⠀⠠⠥
262	$v \in V$	⠧⠀⠈⠑⠀⠠⠧
263	$Y = {B, W}$	⠠⠽⠀⠨⠅⠀⠨⠷⠠⠃⠠⠀⠠⠺⠨⠾
264	$f : X \to Y$	⠋⠸⠒⠀⠠⠭⠀⠫⠕⠀⠠⠽
265	$M_{m \times n} (Z_{2})$	⠈⠰⠠⠍⠰⠍⠈⠡⠝⠐⠷⠸⠰⠠⠵⠆⠾
266	$[x] = {y \in X : y \sim x}$	⠈⠷⠭⠈⠾⠀⠨⠅⠀⠨⠷⠽⠀⠈⠑⠀⠠⠭⠸⠒⠽⠀⠈⠱⠀⠭⠨⠾
267	$F [x]$	⠠⠋⠈⠷⠭⠈⠾
268	$char R$	⠉⠓⠁⠗⠀⠠⠗
269	$r cis θ$	⠗⠉⠊⠎⠀⠨⠹
270	$α β = i d$	⠨⠁⠨⠃⠀⠨⠅⠀⠊⠙
271	$\deg f (x) = n$	⠙⠑⠛⠀⠋⠷⠭⠾⠀⠨⠅⠀⠝
272	$det A = a d - b c \neq 0$	⠙⠑⠞⠀⠠⠁⠀⠨⠅⠀⠁⠙⠤⠃⠉⠀⠌⠨⠅⠀⠼⠴
273	$\dim V = n$	⠙⠊⠍⠀⠠⠧⠀⠨⠅⠀⠝
274	$f^{- 1} (x) = e^{x}$	⠋⠘⠤⠂⠐⠷⠭⠾⠀⠨⠅⠀⠑⠘⠭
275	$f \subset A \times B$	⠋⠀⠸⠐⠅⠀⠠⠁⠈⠡⠠⠃
276	$g (1) = a$	⠛⠷⠂⠾⠀⠨⠅⠀⠁
277	$d = gcd (a, b)$	⠙⠀⠨⠅⠀⠛⠉⠙⠀⠷⠁⠠⠀⠃⠾
278	$X_{i} \cap X_{j} = \emptyset$	⠠⠭⠰⠊⠐⠨⠩⠠⠭⠰⠚⠀⠨⠅⠀⠸⠴
279	$\ker ϕ$	⠅⠑⠗⠀⠨⠋
280	$s - t = l n$	⠎⠤⠞⠀⠨⠅⠀⠇⠝
281	$lcm (a, b)$	⠇⠉⠍⠀⠷⠁⠠⠀⠃⠾
282	$lim_{n \to \infty} f_{n} / f_{n + 1} = (\sqrt{5} - 1) / 2$	⠐⠇⠊⠍⠩⠝⠀⠫⠕⠀⠠⠿⠻⠀⠋⠰⠝⠐⠸⠌⠋⠰⠝⠬⠂⠀⠨⠅⠀⠷⠜⠢⠻⠤⠂⠾⠸⠌⠆
283	$f (x) = \ln x$	⠋⠷⠭⠾⠀⠨⠅⠀⠇⠝⠀⠭
284	$R^{m}$	⠈⠰⠠⠗⠘⠍
285	$\deg (p (x) + q (x)) \leq max (\deg p (x), \deg q (x))$	⠙⠑⠛⠀⠷⠏⠷⠭⠾⠬⠟⠷⠭⠾⠾⠀⠐⠅⠱⠀⠍⠁⠭⠀⠷⠙⠑⠛⠀⠏⠷⠭⠾⠠⠀⠙⠑⠛⠀⠟⠷⠭⠾⠾
286	$d_{min}$	⠙⠰⠍⠊⠝
287	$r = s$	⠗⠀⠨⠅⠀⠎
288	$r$	⠸⠰⠗
289	$f (x) = \sin x$	⠋⠷⠭⠾⠀⠨⠅⠀⠎⠊⠝⠀⠭
290	$r / s \sim t / u$	⠗⠸⠌⠎⠀⠈⠱⠀⠞⠸⠌⠥
291	$b = (2, 2)^{t}$	⠸⠰⠃⠀⠨⠅⠀⠷⠆⠠⠀⠆⠾⠘⠞
292	$v \in R^{2}$	⠧⠀⠈⠑⠀⠈⠰⠠⠗⠘⠆
293	$w$	⠸⠰⠺
294	$x = (x_{1}, \dots, x_{n})$	⠸⠰⠭⠀⠨⠅⠀⠷⠭⠂⠠⠀⠄⠄⠄⠠⠀⠭⠰⠝⠐⠾
295	$A = {x, y}$	⠠⠁⠀⠨⠅⠀⠨⠷⠭⠠⠀⠽⠨⠾
296	$y = (y_{1}, \dots, y_{n})$	⠸⠰⠽⠀⠨⠅⠀⠷⠽⠂⠠⠀⠄⠄⠄⠠⠀⠽⠰⠝⠐⠾
297	$\| x - y \| \leq 4$	⠳⠭⠤⠽⠳⠀⠐⠅⠱⠀⠼⠲
298	$\tilde{σ}$	⠐⠨⠎⠣⠈⠱⠻
299	$A \times B$	⠠⠁⠈⠡⠠⠃
300	$Δ = b^{2} - 4 a c$	⠨⠠⠙⠀⠨⠅⠀⠃⠘⠆⠐⠤⠲⠁⠉
301	$α$	⠨⠁
302	$β$	⠨⠃
303	$⟨ a_{r}, a_{s} ⟩ = δ_{r s}$	⠨⠨⠷⠸⠰⠁⠰⠗⠠⠀⠸⠰⠁⠰⠎⠐⠨⠨⠾⠀⠨⠅⠀⠨⠙⠰⠗⠎
304	$η : G / K \to ψ (G)$	⠨⠱⠸⠒⠀⠠⠛⠸⠌⠠⠅⠀⠫⠕⠀⠨⠽⠷⠠⠛⠾
305	$λ$	⠨⠇
306	$μ_{1} ρ_{1}$	⠨⠍⠂⠨⠗⠂
307	$ν : Z [\sqrt{3} i] \to N \cup {0}$	⠨⠝⠸⠒⠀⠈⠰⠠⠵⠈⠷⠜⠒⠻⠊⠈⠾⠀⠫⠕⠀⠈⠰⠠⠝⠨⠬⠨⠷⠴⠨⠾
308	$π : S \to S$	⠨⠏⠸⠒⠀⠠⠎⠀⠫⠕⠀⠠⠎
309	$ψ$	⠨⠽
310	$w = s cis ϕ$	⠺⠀⠨⠅⠀⠎⠉⠊⠎⠀⠨⠋
311	$A^{'}$	⠠⠁⠄
312	$g^{″}$	⠛⠄⠄
313	$ℓ$	⠈⠰⠇
314	$f : A \to B$	⠋⠸⠒⠀⠠⠁⠀⠫⠕⠀⠠⠃
315	$f : a \mapsto b$	⠋⠸⠒⠀⠁⠀⠫⠳⠒⠒⠕⠀⠃
316	$(\Leftarrow)$	⠷⠫⠪⠶⠶⠾
317	$\emptyset$	⠸⠴
318	$- 3 \notin E$	⠤⠼⠒⠀⠌⠈⠑⠀⠠⠑
319	$C^{*}$	⠈⠰⠠⠉⠘⠈⠼
320	$(g \circ f) (x) = g (f (x))$	⠷⠛⠨⠡⠋⠾⠷⠭⠾⠀⠨⠅⠀⠛⠷⠋⠷⠭⠾⠾
321	$a ∣ b$	⠁⠳⠃
322	$p ∤ a$	⠏⠌⠳⠁
323	$a \land b$	⠁⠈⠩⠃
324	$a \lor b$	⠁⠈⠬⠃
325	$A \cup B$	⠠⠁⠨⠬⠠⠃
326	$x \sim y$	⠭⠀⠈⠱⠀⠽
327	$≅$	⠈⠱⠨⠅
328	$a \neq 0$	⠁⠀⠌⠨⠅⠀⠼⠴
329	$\equiv$	⠸⠇
330	$q ≢ 1 (\mod p)$	⠟⠀⠌⠸⠇⠀⠼⠂⠷⠍⠕⠙⠀⠏⠾
331	$x \geq y$	⠭⠀⠨⠂⠱⠀⠽
332	$B \supset A$	⠠⠃⠀⠸⠨⠂⠀⠠⠁
333	$A ⊄ B$	⠠⠁⠀⠌⠸⠐⠅⠀⠠⠃
334	$W = U \oplus V$	⠠⠺⠀⠨⠅⠀⠠⠥⠫⠉⠸⠫⠬⠻⠠⠧
335	$2 \cdot 4$	⠼⠆⠡⠲
336	$Z_{3} ⋊ Z_{4}$	⠠⠵⠒⠈⠡⠳⠠⠵⠲
337	$△ A B C$	⠫⠞⠀⠠⠁⠠⠃⠠⠉
338	$a ⪯ b$	⠁⠀⠨⠐⠅⠱⠀⠃
339	$⪰$	⠨⠨⠂⠱