310 
Mil. G. T. BENNETT ON THE RESIDUES OE POWERS OF NUMBERS 
m 
m = 5 + 5i = - i{l i) (2 + i) (1 + 2i) N (m) = 50 $ {m) = 16 = 22. 2^ 
H. E. = 4 2 / = Y(mod5) x = X + Y —//(mod 10). 
Generators 4 + i, 9 + 4n 
0 0 
1 
i 
3 1 
0 1 
9 + 4i 
3/ 
2 0 
0 2 
5 + 2'i 
1 
0 0 
0 3 
2 + 3/ 
1 + 4/ 
3 2 
1 0 
4 + / 
2 + Si 
0 3 
1 1 
7 
3 
3 3 
1 2 
8 + 3'i 
3 + 2/ 
2 1 
1 3 
5 + 4/ 
4 + / 
1 0 
2 0 
3/ 
5 + 2/ 
0 2 
2 1 
3 + 2/ 
5 + 4/ 
1 3 
2 2 
9 
6 + / 
2 3 
2 3 
6 + / 
7 
1 1 
3 0 
7 + 2/ 
7 + 2/ 
3 0 
3 1 
i 
8 + 3/ 
1 2 
3 2 
1 + 4/ 
9 
2 2 
3 3 
3 
9 + 4i 
I 
0 1 
(4) (4) (4) 
r= G + 4^■ = — Ml + if (3 + 'll) N (m) = 52 <t> (ni) = 24 = 2. 2^. 3 H. E. = 1 
y ~ Y (mod 2) a? = X + 5 (Y — y) (mod 26). 
Generators 15, 22 + i. 
0 0 
1 1 
0 1 
22 + / 
1 0 
15 
1 1 
10 + / 
2 0 
17 
2 1 
12 + / i 
3 0 
21 i 
3 1 
16 + / 
4 0 
3 
4 1 
24 “1“ i 
5 0 
19 
5 1 
14 + / ■ 
6 0 
25 
6 1 
20 + / 
1 7 0 
11 
7 1 
6 -j- i 
8 0 
9 
8 
4 + / 
9 0 
5 
9 1 
i 
10 0 
23 
10 1 
18 + / 
11 0 
7 
1 11 1 
2 + / 
( 12 ) ( 2 ) 
i 
9 1 
1 
0 0 
2 + / 
11 1 
3 
4 0 
4 + / 
8 1 
5 
9 0 
(3 -j- i- 
7 1 
i 
11 0 
9 
8 0 
10+/ 
1 1 
11 
7 0 
12 + / 
2 1 
14 + / 
5 1 
15 
1 0 
IG "}“ i 
3 1 
17 
2 0 
18 + / 
10 1 
19 
5 0 
20 + / 
6 1 
21 
3 0 
22 + / 
0 1 
23 
10 0 
24 + / 
4 1 
25 
6 0 
(12) (2) 
