Talk:Luhn mod N algorithm: Difference between revisions

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

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

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.

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 {{maths rating|class=start|importance=low|field=number theory}}
+== 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:
+{| class="wikitable"
+|-
+! Original digit !! Doubled !! Reduced
+|-
+| 0 || 0 (00<sub>9</sub>) || 0
+|-
+| 1 || 2 (02<sub>9</sub>) || 2
+|-
+| 2 || 4 (04<sub>9</sub>) || 4
+|-
+| 3 || 6 (06<sub>9</sub>) || 6
+|-
+| 4 || 8 (08<sub>9</sub>) || 8
+|-
+| 5 || 10 (11<sub>9</sub>) || 2
+|-
+| 6 || 12 (13<sub>9</sub>) || 4
+|-
+| 7 || 14 (15<sub>9</sub>) || 6
+|-
+| 8 || 16 (17<sub>9</sub>) || 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.
+[[User:Stevie-O|Stevie-O]] ([[User talk:Stevie-O|talk]]) 13:48, 30 May 2019 (UTC)