Code: PU
P=100 (k=69=7 (mod 31) )
Formulae:
Number N is divisible by 31 iff 7*b+a is divisible by 31
Example:
Number N = 98 76 54 32 08 = 5 14 23 1 8 =
7( 5 14 23 1)+8 =
7(7(5 14 23+1)+8 =
7(7(7( 5 14+23)+1)+8 =
7(7(7(7* 5+14)+23)+1)+8 =
7(7(7* 18+23)+1)+8 =
7(7* 25+1)+8 =
7* 21+8 = 0 (mod 31)
is divisible by 31.
Code: SF 28*10-9*31=1
28(10b+a) = b+28a = b-3a (mod 31)
Formulae:
Number N is divisible by 31 iff b-3a is divisible by 31
Example:
Number N = 68931
6893-3*1 = 6890
689-3*0 =689
68-3*9 = 41
4-3*1 = 1
isn't divisible by 31
Code: SF- 3*10-1*31=-1
3(10b+a) = -b+3a = -(b-3a) (mod 31)
It is the same as above.
