number 18

Code: PU  P=100 (k=82=10 (mod 18) )
Formulae:
Number N is divisible by 18 iff 10*b+a is divisible by 18

Example:
Number N = 98 76 54 32 10 = 8 4 0 14 10 =
10(  8 4 0 14)+10 =
10(10(  8 4 0+14)+10 =
10(10(10( 8 4+0)+14)+10 =
10(10(10(10*8+4)+0)+14)+10 =
10(10(10*  12+0)+14)+10 =
10(10*     12+14)+10 =
10*         8+10 = 0 (mod 18)
is divisible by 18.



Code: PD
P=10, (k=8)
Formulae:
Number N is divisible by 18 iff -8b+a is divisible by 18

Example:
Number N = 54392
-8(      5439)+2 =
-8(-8(    543+9)+2 =
-8(-8(-8(  54+3)+9)+2 =
-8(-8(-8(-8*5+4)+3)+9)+2 =
-8(-8(-8*   0+3)+9)+2 =
-8(-8*      3+9)+2
-8*         3+2 = 14 (mod 18)
isn't divisible by 18.



Code: PS, CR
P=9*10, (k=9)
Formulae:
Number N is divisible by 18 iff remainder from division by 90 is divisible by 18

Example:
Number N = 68940 with base P=10
B=[6], C=?, A=[8,9,4,0]
B=[0]/9#[6*10+8]=[0,68], C=6, A=[9,4,0]
B=[0,63]/9#[5*10+9]=[0,7,59], C=5, A=[4,0]
B=[0,0,684]/9#[5*10+4]=[0,0,76,54], C=5, A=[0]
B=[0,0,72,414]/9#[0]=[0,0,8,46,0], C=0, A=[]
least significant digit of 8 46 0 is 0, so N is divisible by 18
or (other here eg. 68=63+5, 63 stands by and 5 movies to less significant value).
[6, 8, 9, 4 | 0] = [0, 63, 54, 54 | 0] = 9*[0, 7, 6, 6] 0
[0, 7, 6 | 6] = [0, 0, 72 | 46] = 9*[0, 0, 8] 46
[0, 0 | 8] = 9*[0] 8