Code: PU
P=100 (k=83=15=-2 (mod 17) )
Formulae:
Number N is divisible by 17 iff 15*b+a = -2b+a is divisible by 17
Example:
Number N = 98 76 54 32 10 = 13 8 3 15 10 =
-2( 13 8 3 15)+10 =
-2(-2( 13 8 3+15)+10 =
-2(-2(-2( 13 8+3)+15)+10 =
-2(-2(-2(-2*13+8)+3)+15)+10 =
-2(-2(-2* 16+3)+15)+10 =
-2(-2* 5+15)+10
-2* 5+10 = 0 (mod 17)
is divisible by 17.
Code: PD
P=10, (k=7)
Formulae:
Number N is divisible by 17 iff -7b+a is divisible by 17
Example:
Number N = 54391
-7( 5439)+1 =
-7(-7( 543+9)+1 =
-7(-7(-7( 54+3)+9)+1 =
-7(-7(-7(-7*5+4)+3)+9)+1 =
-7(-7(-7* 3+3)+9)+1 =
-7(-7* (-1)+9)+1
-7* (-1)+1 = 8 (mod 17)
isn't divisible by 17.
Code: SF 12*10-7*17=1
12(10b+a) = b+12a (mod 17)
Formulae:
Number N is divisible by 17 iff b+12a is divisible by 17
Example:
Number N = 68941
6894+12*1 = 6906
689+12*8 = 762
76+12*2 = 100
10+12*0 = 10
isn't divisible by 17
This rule is equivalent the next one.
Code: SF- 5*10-3*17=-1
5(10b+a) = -b+5a = -(b-5a) (mod 17)
Formulae:
Number N is divisible by 17 iff b-5a is divisible by 17
Example:
Number N = 67915
6791-5*5 = 6766
676-5*6 =646
64-5*6 = 34 = 2*17
is divisible by 17
