The mathematics of credit cards: Luhn's algorithm

Mathematics has always interested and fascinated man, since, thousands of years ago, the village chief had to evaluate whether to attack another village or flee (based on the superiority or numerical inferiority of his warriors compared to the enemy ones) up to nowadays, where mathematics is the basis of the functioning of computers, tablets, smartphones and guarantees the security and privacy of our passwords and our home banking operations.
The algorithm of the German engineer that I describe in this activity has always struck me for its effectiveness and simplicity. Hans Peter Luhn, using very few concepts of elementary mathematics (and being an engineer it could not be otherwise), managed to earn a lot of money with this idea.