300 MR. G. T. BENNETT ON THE RESIDUES OF POWERS OF NUMBERS 
'}ii — 3 ”1“ 2'i 
= 2 + 3 ^ 
N {in) = 13 43 {m) = 12 = 23.3 
N (m) =13 43 (m) = 12 = 23.3 
H.E=12 5c = X + 5Y (mod 13). 
H.E = 12 5C = X + 8Y(mod 13). 
Generator 2. 
0 
1 
2 ;l 
4 5 
6 7 
8 
9 
10 
11 
1 
2 
4 8 
3 6 
12 11 
9 
5 
10 
7 
1 
1 
2 3 
4 5 
6 
7 
8 9 
10 
11 
12 
0 
1 4 
2 9 
5 
11 
3 8 
10 
7 
6 
( 12 ) 
( 12 ) 
m z=. 4: i N (??i) = 17 43 (m)=16 = 2^ H.E = 16 a; = X + 13Y (mod 17). 
m—l+4i N(m)=17 c]&(m)=16 = 2^ H.E =16 a; = X + 4Y (mod 17). 
Generator 3. 
N 
0 1 2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
(16) 
13 9 
10 
13 
5 
15 
11 
16 
14 
8 
7 
4 
12 
2 
6 
N 
1 
2 
3 
4 
5 
6 
7 
8 9 
10 
11 
12 
13 
14 
15 
16 
0 
14 
1 
12 
5 
15 
11 
10 2 
3 
7 
13 
4 
9 
6 
8 
(16) 
m = 3 + = (1 + 7) 3 N {m) =18 4) (m) =8 = 2^ H.E = 8 y = Y (mod 3) 
a: = X + 3 (Y — 2 /) (mod 6). 
Generator 1 +27. 
0 
1 
i 
2 
1 
l4-2i 
1 
0 
o 
1 + 2/ 
1 ' 
3 
4 + 'i 
2 + '/ 
5 
4 
3 + 2/ 
0 i 
0 
2 + 
4 + / 
o 
O 
6 
3 + 2i 
5 
4 
i 
5 + 2t 
5 + 2/ 
( 8 ) 
( 8 ) 
