Fermat's little theorem

There are the experimental sciences (physics, chemistry, biology, etc.) and mathematics, you may think. Well, no! In mathematics too, we carry out experiments, and even testing and manipulations (see Tangente Éducation 30). To divide, we test the possible quotients. At a higher level, how many conjectures, throughout history, have been stated tentatively after many attempts! Today, mathematical experiments take new forms, due to the development of computer science. What a wonderful tool the computer is to simulate, make trials, test conjectures or model a phenomenon! We must not forget, afterward, to prove…

Although less known than its "big brother", Fermat's Little Theorem is, in turn, a gem of arithmetic, and all the more useful! That an abstract mathematical result finds, three hundred years after being established, fundamental applications, is surprising! Yet such is the case, in particular in the field of information exchange on the Internet. This small gem, uncovered by the "masterful magistrate" Pierre de Fermat, provides fundamental cryptographic algorithms, the most well-known being RSA. A gem that hasn't finished making waves: there are still gray areas and conjectures to prove!