Code: PU
P=100 (k=87=9 (mod 13) )
Formulae:
Number N is divisible by 13 iff 9*b+a = -4b+a is divisible by 13
Example:
Number N = 98 76 54 32 09 = 7 11 2 6 9 =
9(7 11 2 6)+9 =
9(9(7 11 2+6)+9 =
9(9(9(7 11+2)+6)+9 =
9(9(9(9* 7+11)+2)+6)+9 =
9(9(9* 9+2)+6)+9 =
9(9* 5+6)+9
9* 12+9 = 0 (mod 13)
is divisible by 13.
Code: PD
P=10, (k=3)
Formulae:
Number N is divisible by 13 iff -3b+a is divisible by 13
Example:
Number N = 54391
-3( 5439)+1 =
-3(-3( 543+9)+1 =
-3(-3(-3( 54+3)+9)+1 =
-3(-3(-3(-3*5+4)+3)+9)+1 =
-3(-3(-3* 2+3)+9)+1 =
-3(-3* 10+9)+1
-3* 5+1 = 12 (mod 13)
isn't divisible by 13.
Code: SN, PD in P=1000 (k=1 special) 1001 = 7*11*13
Compare with divisibility rule by 7
Formulae:
Number N is divisible by 13 iff remainder from division by 1001 is divisible by 13
Code: SF 4*10-3*13=1
4(10b+a) = b+4a (mod 13)
Formulae:
Number N is divisible by 13 iff b+4a is divisible by 13
Example:
Number N = 68941
6894+4*1 = 6898
689+4*8 = 721
72+4*1 = 76
7+4*6 = 31 = 2*13+5
isn't divisible by 13, but the remainder is other than 5
Code: SF- 9*10-7*13=-1
9(10b+a) = -b+9a (mod 13)
Formulae:
Number N is divisible by 13 iff b-9a is divisible by 13
Example:
Number N = 67912
6791-9*2 = 6773
677-9*3 =650
65-9*0 = 65 = 5*13
is divisible by 13
