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

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