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“Who discover how to calculate the check digits of the accounts of the Bank Santander, will get a distinction”. Thus was finished one of his classes the professor of Abstract Algebra Applied when he was in the last year of the race. But before revealing, as he ended this story, we must clarify the following, what are the check digits?

The check digits are numbers (sometimes letters) that accompany some data , as for example, the ID, the barcode, the numbers of the current account or the ISBN of the books. Its purpose is to control the accuracy of the data to which they are attached, that is to say, make element verifier .

These digits are obtained as a result of a mathematical operation on the numbers to which they are associated. is For security reasons this operation is usually secret , but with mathematical methods a little bit advanced you can get to decipher.

National Identity

the closest example of The use of the check digit as we have in the National Identity Document (DNI).

A ID. If you write a bogus number, the letter probably we delatará

The letter of the DNI, which in principle seems to be something totally random is no more that a check digit is included for security reasons. is If you write an ID fake or we were wrong to put any number, the more likely it is that the letter is written does not match what it should be and thus detects the falsity of the document.

How do you get the letter of the DNI?

To calculate the letter of the DNI we divide the corresponding number (8 digits without letter) between 23 and then we take the rest of the division. For example, if we have the ID whose number is 12345678 when divided by 23 has to be

12345678 = (23 x 536768) + 14,

and therefore the rest of the division is 14. Since we do a division by 23 the remainder will always be a number between 0 and 22.

Then, to each number from 0 to 22 is made to correspond to a letter according to the following table:

And so it is obtained that the letter corresponding to the ID number 12345678 is the Z. you Can do the test with your ID .

check Digits in the current accounts

Imagine that you make a transfer to a number of account, and you’re wrong when you write a digit , it could happen, because the current accounts are not exactly short. This failure could cause you to send the money to another person who probably wouldn’t even know it, which, ultimately, would that cause you to lose money. But fear not, because the mathematics come to the rescue to avoid such embarrassing situation.

current accounts incorporate several digits are control digits , and that as in the case of the DNI are obtained by performing a account secret. The use of these digits, in the past 2 and now 4, makes it difficult to generate account numbers to be false-that do not correspond to a real account – and it also has the advantage of enabling the detection of errors in the writing of an account number.

Digits that appear in the current accounts.

so if you make a mistake when typing an account number, very probably, the digit of control of the account will not be those which fall to them , so that it will detect your error and that transfer will not be performed.

There are mathematical tools that allow you to not only detect that an error has been made, if not, that make it possible to identify the error that has been committed and may as well fix it, it seems like magic but in truth are nothing more than math. is Are what are known as codes alarms errors .

In relation to the story with which we began the article, my colleagues and a server, we were able to decipher how to calculate the check digits in the accounts of Ibercaja. However, the Banco Santander we resisted.

Victor M. Manero is a professor of the University of Zaragoza and member of the commission of disclosure of the Royal Mathematical Society of Spain.

The ABCdario Math is a section that emerges from the collaboration with the Commission of Disclosure of the Royal Mathematical Society of Spain (RSME).