Malunga nokomelela kwe-IBAN04
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Njengoko kuyaziwa, i-IBAN yaseJamani iqulethe ikhowudi yelizwe (DE), idijithi yokutshekisha idijithi ezimbini (ngokwe- ISO 7064 ), ikhowudi yebhanki (i-8-digit) kunye nenombolo ye-akhawunti (kuquka inombolo ye-akhawunti engaphantsi, Iidijithi ezili-10, ezilahlekileyo zizaliswe ngooziro abakhokelayo) kwaye ke ngoko inamanani angama-22. Ukubala idijithi yokutshekisha, ebizwa ngokuba yi-BBAN (ikhowudi yebhanki kunye nenombolo ye-akhawunti) kunye nekhowudi yelizwe lamanani \(1314\) yeJamani kunye nedijithi yokutshekisha \(00\) ) zenziwe.

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Umzekelo, ikhowudi yebhanki engu-21050170 kunye nenombolo ye-akhawunti 12345678 ibuyisela i-BBAN 210501700012345678, eyandisiweyo kunye nekhowudi yelizwe kunye nedijithi yetshekhi 00 emva koko isiphumo \ \(98 - (x \mod 97)\) \(x = 210501700012345678131400\) ye-8) iphi ngoku: \(98 - (x \mod 97)\) . Akumangalisi ukuba oku kwahlulwe ngo \(97\) . Njengelona nani likhulu elinokubakho elinemivo emibini ephambili, iqaphela amangeniso angachanekanga njengamasuntswana atshintshiweyo ngeyona ndlela inkulu enokwenzeka. Ngoku sibonisa ezi ngxelo zilandelayo:

1. Ukutshintsha idijithi enye ye-IBAN esebenzayo kuya kukhokelela kwi-IBAN engasebenziyo.
2. Ukutshintsha amasuntswana amabini e-IBAN esebenzayo kunokubangela i-IBAN esebenzayo.
3. Ukuba izikhundla ezibini ezahlukeneyo ze-IBAN ezisebenzayo ziyatshintshwa, i-IBAN engasebenziyo iyadalwa.
4. Ukuba utshintshanisa izikhundla ezimbini ezahlukeneyo ze-IBAN esebenzayo kabini, i-IBAN esebenzayo ingaphumela.

Vumela $$A = DE P_1 P_2 N_1 N_2 N_3 N_4 N_5 N_6 N_7 N_8 N_9 N_{10} N_{11} N_{12} N_{13} N_{14} N_{15} N_{16} N_{17} N_{18}$$ esebenzayo IBAN.

Emva koko $$A_B = N_1 N_2 N_3 N_4 N_5 N_6 N_7 N_8 N_9 N_{10} N_{11} N_{12} N_{13} N_{14} N_{15} N_{16} N_{17} N_{18} 131400$$ ehambelana nayo (yandiswe ngekhowudi yelizwe enenombolo-DE kunye nedijithi yokutshekisha \(00\) ).

1. Guqula ngoku \(N_k\), yi \(A_B^* = A_B + l \cdot 10^{24-k}\) kunye \(1 \leq k \leq 18\) kwaye \((-1) \cdot N_k \leq l \leq 9-N_k \wedge l \neq 0\). Nge \( P = 98 - (A_B \mod 97) \) kodwa kunjalo \(P^* = 98 - \left((A_B + l \cdot 10^{24-k}) \mod 97\right) \). Isebenza ngokubanzi kwi \( a \equiv a' \mod m, b \equiv b' \mod m \): \(a + b \equiv a' + b' \mod m\). Nge \(A_B \equiv R_1 \mod 97\) kwaye \(l \cdot 10^{24-k} \equiv R_2 \mod 97\) yi \( (A_B + l \cdot 10^{24-k}) \equiv R_1 + R_2 \mod 97 \). Kodwa ngoku kunjalo \( 0 < R_2 < 97 \) kwaye njalo \( P^* = 98 - (R_1+R_2) \neq 98 - R_1 = P \) kwaye ke ngoko \( P_1 \neq P_1^* \vee P_2 \neq P_2^* \). Oku kushiya utshintsho olunye kuphela olunokwenzeka lwedijithi ukusuka \( P \) ukuya \( P^* \neq P \). Apha kodwa \( N_k \) ihlala ingatshintshwanga, itshekhisum yenziwe \( P \neq P^* \).
2. Ezi IBAN zimbini zilandelayo ziyasebenza:
   $$\begin{align} A_1 = DE89207300\boldsymbol{\color{red}01}0012345674 \\ A_2 = DE89207300\boldsymbol{\color{red}98}0012345674 \end{align}$$ Le kulapho uthatha khona inzuzo$ , ukuba sonyuse amanani amabini ameleneyo kwi \(A_1\) nge \(97\) . Ukongeza, i-IBAN ayisebenzi ngokusesikweni kuphela, kodwa iikhowudi zebhanki ezisisiseko 20730001 kunye ne-20730098 zikhona ngokwenene.
3. Sizama kuqala, \( N_{k_1} \) kwaye \( N_{k_2} \) ukutshintsha. Okokuqala kukuba \( P = 98 - (A_B \mod 97) \) njenge \(P^* = 98 - \left((A_B + l \cdot 10^{24-k_1} - l \cdot 10^{24-k_2}) \mod 97\right) \) kunye \(l = N_{k_2} - N_{k_1}\) kwaye \(1 \leq k_1, k_2 \leq 18\). Ngoku kungenxa
   
   $$\begin{array} {|c|c|} \hline k & R = 10^{24-k} \mod 97 \\ \hline 1 & 56 \\ \hline 2 & 25 \\ \hline 3 & 51 \\ \hline 4 & 73 \\ \hline 5 & 17 \\ \hline 6 & 89 \\ \hline 7 & 38 \\ \hline 8 & 62 \\ \hline 9 & 45 \\ \hline 10 & 53 \\ \hline 11 & 15 \\ \hline 12 & 50 \\ \hline 13 & 5 \\ \hline 14 & 49 \\ \hline 15 & 34 \\ \hline 16 & 81 \\ \hline 17 & 76 \\ \hline 18 & 27 \\ \hline \end{array}$$
   \( \forall k_1 \neq k_2 \in \left\{ 1, \ldots, 18 \right\} : R_{k_1} \neq R_{k_2}\). Kunjalo ke \( P \neq P^* \). Ke kuya kuhlala kujongwe oko \(P_n\) kwaye \(N_k\) kunye \( 1 \leq n \leq 2 \) kwaye \( 1 \leq k \leq 18 \) urhwebo. Ingayiyo \(P = 98 - (A_B \mod 97)), (R_1 = (A_B \mod 97)\), \(P^* = 98 - (A_B + (l \cdot 10^{24-k}) \mod 97)\), \(R_2 = (A_B + (l \cdot 10^{24-k}) \mod 97)\). Ekubeni thina \(A_B\) ngeenxa zonke \(l \cdot 10^{24-k}\) kufuneka sitshintshe \(P_1\) okanye \(P_2\) ngeenxa zonke \(-l\), ngoko \(P\) ngeenxa zonke \(-10^m l\) kunye \(m \in \{0,1\}\) utshintsho: Emva koko \(P^* = 98 - R_2\) kodwa kwakhona \(P^* = P - 10^m l = 98 - R_1 - 10^m l\), ngenxa yoko \(R_2 = R_1 + 10^m l,\) kwaye njalo
   $$((A_B \mod 97) + (l \cdot 10^{24-k} \mod 97)) \mod 97 = (A_B \mod 97) + 10^m l$$ Nangona kunjalo, le nxaki ayizange izaliseke, njengoko umbhalo olandelayo ubonisa:
   
   

   See the Pen IBAN FORMULA CHECK by David Vielhuber (@vielhuber) on CodePen.

   Oku kushiya kuphela utshintsho olunokwenzeka lwe \(P_1\) kwaye \(P_2\). Apha kodwa \( N_k \) ihlala ingatshintshwanga, itshekhisum yenziwe \( P \neq P^* \).
4. Ezi IBAN zimbini zilandelayo ziyasebenza:
   $$\begin{align*}A_1 = DE\boldsymbol{\color{red}8}\boldsymbol{\color{green}3}20220800\boldsymbol{\color{red}1}000000\boldsymbol{\color{green}0}00 \\ A_2 = DE\boldsymbol{\color{red}1}\boldsymbol{\color{green}0}20220800\boldsymbol{\color{red}8}000000\boldsymbol{\color{green}3}00\end{align*}$$ Apha, kwakhona, i-BIC 20220800 ikhona ngokwenene.