RSA Encryption... thanks to Fermat?

You may not know about the RSA encryption, but you certainly use it every day. It's the encryption with very long numbers that e-mail accounts and banks use to avoid being read by third parties.

This video below tells you how it woks in a beautiful and very simple way. You can then read more about it here, if you are interested.

For me, the most beautiful part of the video is that it tells how the RSA encryption was derived from a Theorem by Fermat (not his "Last Theorem", but the "Little Theorem"). It states that if you have a number x, and you elevate it to the power of P (P being prime), then

x^P - x -> must be a multiple of P.

Example: 4⁵ - 4 = 1024 - 4 = 1020, multiple of 5.

What a beautiful result, what simplicity - and like the video says, how useful it became!