PROBABILITÉS et ARITHMÉTIQUE : 2 oraux SPECTACULAIRES ! (sup/spé)

Two math oral exams where probability can be used to prove non-trivial arithmetic results... very easily! Euler's indicator / Eulerian product. One IMT (Mines-Télécom) oral exam is accessible from the first year, and one Mines-Ponts oral exam for second year students that relates prime numbers to the Riemann Zeta function. 00:00 Introduction 01:15 Oral presentation 1 (IMT). Euler Indicator 04:34 Solution to exercise 1 question 1) 06:08 exercise 1 question 2) 12:50 exercise 1 question 3) 18:32 Statement to exercise 2 (Mines-Ponts MP) 22:18 exercise 2 question 1) 24:12 exercise 2 question 2) 27:10 exercise 2 question 3) 33:00 2 words on the Zeta function