FOR ANY COMPOSITE MODULUS, REAL OR COMPLEX 
295 
This gives eight solutions 
^=(1. 0. 0)=17, 
= (3. 0. 0)= 13, 
= (1. 2. 0)= 7, 
= (3.2.0)= 3, 
= (1. 0. 1)= 1+27, 
= (3. 0. 1) = 17 + 27, 
= (1. 2. l) = ll +27, 
= (3. 2. 1)= 7 + 27. 
Hence there are eight solutions of the congruence 
VIZ., 
= 13 + 167 (mod 20), 
7 + 47 17 + 47 7 + 147 
3 + 67 13 + 67 3 + 167 
and hence there are 32 solutions of the congruence 
viz.. 
2.'r^ = 26 + 327 (mod 40), 
7 + 47 
17+ 47 
7 + 147 
27 + 47 
37 + 47 
27 + 147 
7 + 247 
17 + 247 
7 + 347 
27 + 247 
37 + 247 
27 + 347 
3+ 67 
13 + 67 
3 + 167 
23 + 67 
33 + 6i 
23 + 167 
3 + 267 
13 + 267 
3 + 367 
23 + 267 
33 + 267 
23 + 367 
17 + 147 
13 + 167 
17 + 147 
37 + 147 
17+ 347 
37 + 347 
13 + 167 
33 + 167 
13 + 367 
33 + 367 
