Talk:Luhn mod N algorithm

Problems if N is odd

While implementing this algorithm, I noticed an interesting property for odd N:

Consider the case of base-9. For doubled positions, this occurs:

Original digit	Doubled	Reduced
0	0 (009)	0
1	2 (029)	2
2	4 (049)	4
3	6 (069)	6
4	8 (089)	8
5	10 (119)	2
6	12 (139)	4
7	14 (159)	6
8	16 (179)	8

This means that, for base-9, e.g. both '1' and '5' in doubled positions are equivalent. This has the following consequences for odd N:

• The algorithm cannot detect all single-digit errors; "17" and "57" both have valid check digits for _sum_ ≡ 0 (mod 9)
• If it is necessary to have the computed value be in a "doubled" position, it is not be possible to obtain the required modulo sum for all input cases.

Stevie-O (talk) 13:48, 30 May 2019 (UTC)