10/13/17

number 27

Code: PU  
P=100 (k=73=19 (mod 27) )

Formulae:
Number N is divisible by 27 iff 19*b+a = -8*b+a is divisible by 27

Example:
Number N = 98 76 54 32 19 = 17 22 0 5 19 =
-8(  17 22 0 5)+19 =
-8(-8( 17 22 0+5)+19 =
-8(-8(-8(17 22+0)+5)+19 =
-8(-8(-8(-8*17+22)+0)+5)+19 =
-8(-8(-8*   21+0)+5)+19 =
-8(-8*      21+5)+19 =
-8*         26+19 = 0 (mod 27)
is divisible by 27.



Code: SF  19*10-7*27=1
19(10b+a) = b+19a = b-8a (mod 27)
Formulae:
Number N is divisible by 27 iff b+19a = b-8a is divisible by 27

Example:
Number N = 68931
6893-8*1 = 6885
 688-8*5 = 648
  64-8*8 = 0
is divisible by 27



Code: SF-  8*10-3*27=-1
8(10b+a) = -b+8a = -(b-8a) (mod 27)
It is the same as above