FOR ANY COMPOSITE MODULUS, REAL OR COMPLEX. 
1 + i 
2i 
- 2 + 2^ = 37 + 2i 
35 + o9i = 35 
35 + 357 = 5 + 2i 
3 + 77 = 33 4- i 
32 + 347 = 2 +7 
1 + 37= 16 
16 + 167 = 13 + 7 
12 + 47 = 33 + 27 . 
31 + 357 = 1 + 27 
- 1 + 37 = 14 
14 + 14i ^ 35 + 2i (uiod. 9 + 6'i) 
33 + 377 = 18 + 7 
17 + 197 = 29 + 7 
28 + 307 = 22 
22 + 227 = 10 + 7 
9 + 117 = 15 + 27 
13 + 177 = 10 + 27 
8 + 127 = 29 
29 + 297 = 8 + 27 
6 + 107 = 12 + 7 
11 + 137 = 32 + 7 
31 + 337 = 1 
In the two special cases 
(i.) m = a + /37 
X + 7Y = X (mod a + /37) and x 
is determined by 
a; = X - Y («« + (B^') (mod + /3^). 
(ii.) m = cl 
X + 7Y =. X iy (mod d) and x and y 
are given by 
a: = X (mod d), 
y = Y (mod d). 
2 K 
249 
MDCCCXCIII.-A, 
