Article : Le sujet dont vous êtes l’auteur - Colegiul National B.P. Hasdeu (Buzau, Roumanie)

Article
Résumé de la production
The work consists of two problems proposed by the students themselves.
In the first problem, the authors consider this question: “given an n×n table and a prime number p, in how many ways the table can be filled with integer numbers such that all the products on each row and each column is p or -p?”.
In the second problem, the question to be answered is: “given a product N = p_1 p_2 ... p_n of different prime numbers, in how many ways N can be written as x^2-y^2, where x and y are positive natural numbers?”
Both problems are solved in the work. Some simulations with the program C++ are also given
Mots clés
simulation
répartition des nombres premiers
combinatoire