Code: PU
P=100 (k=85=10 (mod 15) )
Formulae:
Number N is divisible by 15 iff 10*b+a = -5b+a is divisible by 15
Example:
Number N = 98 76 54 32 05 = 8 1 9 2 0 =
10( 8 1 9 2)+0 =
10(10( 8 1 9+2)+0 =
10(10(10( 8 1+9)+2)+0 =
10(10(10(10*9+1)+9)+2)+0 =
10(10(10* 1+9)+2)+0 =
10(10* 4+2)+0
10* 12 = 0 (mod 15)
is divisible by 15.
Code: PD
P=10, (k=5)
Formulae:
Number N is divisible by 15 iff -5b+a is divisible by 15
Example:
Number N = 54395
-5( 5439)+5 =
-5(-5( 543+9)+5 =
-5(-5(-5( 54+3)+9)+5 =
-5(-5(-5(-5*5+4)+3)+9)+5 =
-5(-5(-5* 9+3)+9)+5 =
-5(-5* 3+9)+5
-5* 9+5 = 5 (mod 15)
isn't divisible by 15.
The rule is common in both cases, but there are different base P, so they are different rules.
Code: CR P=10*3= 30
Formulae:
Number N is divisible by 15 iff least significant digit is 0 or 15 in base P=30
Example:
Number N = 68940 with base P=10
B=[6], C=?, A=[8,9,4,0]
B=[6]/3#[0*10+8]=[2,8], C=0, A=[9,4,0]
B=[0,66]/3#[2*10+9]=[0,22,29], C=2, A=[4,0]
B=[0,21,57]/3#[2*10+4]=[0,7,19,24], C=2, A=[0]
B=[0,6,48,54]/3#[0]=[0,2,16,18,0], c=0, A=[]
least significant digit of 2 16 18 0 is 0, so N is divisible by 15
