324 
J\1R. G. T. BENNETT ON THE RESIDUES OF POWERS OP NUMBERS 
m=94-2i= -?:(2 + ?:)(l + 4{) 2 + 9^■ = (1-{- 22) (4+ 2 ) 7 + fi 2 = (2 + 2 ) (4 + 2 ) 
or 6 + 72= - 2 (1 + 22 ) (1 + 42). 
For all N ( 222 ) = 85 (to) = 64 = 2®. 2^ H.E. = 16. 
2)2 := 9 + 2i rr = X + 38Y (mod 85) 222 = 2 + 92 
2)2 = 7 + 62 .r = X + I 3 Y (mod 85) 2)2 = 6 + 7i 
rr = X + 47Y (mod 85) 
.22 = X + 72Y (mod 85). 
Generators 3, 52. 
0 0 
1 
8 0 
16 
0 1 
52 
8 1 
67 
0 2 
69 
8 2 
84 
0 3 
18 
8 3 
33 
1 0 
3 
9 0 
48 
1 1 
71 
9 1 
31 
1 2 
37 
9 2 
82 
1 3 
54 
9 3 
14 
2 0 
9 
10 0 
59 
2 1 
43 
10 1 
8 
2 ' 2 
26 
10 2 
76 
2 3 
77 
10 3 
42 
3 U 
27 
11 0 
7 
3 1 
44 
11 1 
24 
3 2 
78 
11 2 
58 
3 3 
61 
11 3 
41 
4 0 
81 
12 0 
21 
4 1 
47 
12 1 
72 
4 2 
64 
12 2 
4 
4 3 
13 
12 3 
38 
5 0 
73 
13 0 
63 
5 1 
56 
13 1 
46 
5 . 2 
22 
13 2 
12 
.'■) 3 
39 
13 3 
29 
6 0 
49 
14 0 
19 
6 1 
83 
14 1 
53 
6 2 
66 
14 2 
. 36 
6 3 
32 
14 3 
' 2 
7 0 
62 
15 0 
57 
7 1 
79 
15 1 
74 
7 2 
28 
15 2 
23 
7 3 
11 
15 3 
6 
1 
1 
1 
0 0 
2 
14 3 
3 
1 0 
4 
12 2 
6 
15 3 
7 
11 0 
8 
10 1 
9 
2 0 
11 
7 3 
12 
13 2 
13 
4 3 
14 
9 3 
16 
8 0 
18 
0 3 
19 
14 0 
21 
12 0 
22 
5 2 
23 
15 2 
24 
11 1 
26 
2 2 
27 
3 0 
28 
7 2 
29 
13 3 
31 
9 1 
32 
6 3 
33 
8 3 
36 
14 2 
37 
1 2 
38 
12 3 
39 
5 3 ! 
41 
11 ■ 3 1 
42 
10 3 
43 
2 1 
44 
3 1 
46 
13 1 
47 
4 1 ' 
48 
9 0 
49 
6 0 
52 
0 1 
53 
14 1 
54 
1 3 
56 
5 1 
57 
15 0 
58 
11 2 
59 
10 0 
61 
3 3 
62 
7 0 
63 
13 0 
64 
4 2 
66 
6 2 
67 
8 1 
69 
0 2 
71 
1 1 
72 
12 1 
73 
5 0 
i 74 
15 1 
i 76 
10 2 
7 i 
2 3 
78 
3 2 
: 79 
7 1 
: 81 
4 0 
82 
9 2 ■ 
i 83 
6 1 
84 
8 2 1 
(16) (4) 
(16) (4) 
(16) (4) 
(16) (4) 
