FOR ARY COMPOSITE MODULUS, REAL OR COMPLEX. 
261 
and 
J: {2 -f 0 = (1 H" 0 (iiTtocl 3) 
I' = 2 ^, 
gives 
which is not a real number. 
The following table gives,the indices of the 72 numbers. 
0 
1 
2 
1 
2 + i 
5 + ?: 
8 + f 
2 
3 + a 
7i 
6 + i 
3 
2 + 2i 
2 + 5i 
00 
+ 
4 
2 + 6^ 
8 + 3?’ 
5 
5 
7 + 
4 + 5?: 
1 + 7n 
6 
Hi 
3 + 5? 
6 + 2? 
7 
1 + 7i 
1 + 4/ 
1 +i 
8 
4 + 6^■ 
7 
1 + 3?: 
9 
2 + 7i 
5 + 7i 
S + 7i 
10 
6 + 7i 
3 + i 
4^ 
11 
5 + 2^ 
5 + 5^■ 
5 + Hi 
12 
8 
5 + 6? 
2 + Si 
13 
7 + 8?: 
4 + 8?: 
1 + 8?: 
14 
6 + 5?: 
2^■ 
3 + 8?' 
15 
7 + 7^ 
7 + 4^ 
7 + f 
16 
7 + Si 
1 + 6^■ 
4 
17 
2 + 4? 
5 + 4{ 
8 + 4?' 
18 
i 
6 + 4^ 
3 + 7i 
19 
8 + 2^ 
8 + bi 
8 + Hi 
20 
5 + 3^ 
2 
8 + 6?: 
21 
7 + 2i 
4 + 2i 
1 + 2i 
22 
3 + 2i 
6 + 8?' 
5i 
23 
4 + 7i 
4 + 4^ 
4 + i 
0 
1 
4 + Si 
7 + 6?: 
[The pair of indices for any number are found at the end of the row and at the head 
of the column in which the number is situated. 
Thus 
1 + 8^ = (2 + 0^^ 4* -lO' ll) ] 
