We continued looking at Book VII, Book VIII and Book IX. To be precise we started with the Euclidean Division Algorithm and how to compute the greatest common divisor of two given numbers. Read carefully the commentaries of:
We then moved on and we commented the following propositions: Proposition 14, which Victor Katz reads as a version of the Fundamental Theorem of Arithmetic, that is "every number can be uniquely factored into product of primes." We then ended the lecture with Euclid's famous proof about the infinitude of prime numbers:
Comment: Prime numbers are at the base of our encription systems for all secure transactions that we do over the Internet. Do you know for instance how RSA works? If not, this is a good idea for a topic for your final project. It boils down to Fermat's Little Theorem.
Click on the above links to go directly to the proofs and commentaries of the results.