304 
MR. G. T. BENNETT ON THE RESIDUES OF POWERS OF NUMBERS 
m= 6 =-^(1+^)“ 3 N(m) = 36 <I> (w) = 16 = 2. 2" H. E. = 8 
ic = X (mod 6) y = Y (mod 6). 
Generators 1 + Ai, 4 + 3i. 
0 
0 
1 
0 
1 
4 + -Si 
1 
0 
l + Ai 
1 
1 
4 + i 
2 
0 
3 + 2i 
2 
1 
bi 
3 
0 
l+2i 
! 3 
1 
4 + 
4 
0 
5 
4 
1 
2 + 3i 
.5 
0 
5 + 2i 
5 
1 
2 + bi 
6 
0 
3 + 4i 
6 
1 
i 
7 
0 
.5 + 4i 
7 
1 
2 + t 
i 
6 
1 
bi 
2 
1 
1 
0 
0 
l + 2i 
3 
0 
l+4i 
1 
0 
2 + i 
7 
1 
2 + 3i 
A 
1 
2 + bi 
b 
1 
3 + 2i 
2 
0 
S + Ai 
6 
0 
A + i 
1 
I 
4 -|- 
0 
1 
A + bi 
3 
1 1 
5 
4 
0 
5 +2d' 
5 
0 i 
.5 + 42 
7 
0 1 
(8) (2) (8) (2) 
m = 6 + ^ N (m) = 37 
m = 1 + 6^' N {m) = 37 
(I) (m) = 36 = 22 3^ H. E. = 36 = X + 3lY (mod 37). 
$ (m) = 36 = 21 32 H. E. = 36 x = X+ 6Y (mod 37). 
Generator 2. 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
1 
2 
4 
8 
16 
32 
27 
17 
34 
31 
25 
13 
26 
15 
30 
23 
9 
18 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
35 
33 
29 
21 
5 
10 
20 
3 
6 
12 
24 
11 
22 
7 
14 
28 
19 
(36) 
(36) 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
0 
1 
26 
2 
23 
27 
32 
3 
16 
24 
30 
28 
11 
33 
13 
4 
h- 
/ 
17 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 ' 
! 
35 
25 
22 
31 
15 
29 
10 
12 
6 
34 
21 
14 
9 
5 
20 
8 
19 
IS 
I 
(36) 
