BINOMIAL COEFFICIENTS IN MODULAR ARITHMETIC - A MATHEMATICAL SOLUTION TO MUSICAL QUESTIONS

In this seminar we are linking modular binomial coefficients to periodic sequences with modular integer values. In the context of serialism, the romanian composer Anatol Vieru used such sequences to compose several musical pieces. We will introduce the main properties of periodic sequences and we will explain the link between them and the binomial coefficients in Z/mZ. This allows to use tools such as Kummer's Theorem to answer some questions arisen from Vieru's observations.