Propriedades aritméticas dos coeficientes binomiais

Abstract

The objective of this study is to gather and bring to the attention of the public that appreciates patterns in numbers, whether high school or college students, interesting characteristics of binomial coefficients, as well as some of their applications within Mathematics itself. At first, it presents the definition of these special numbers as coefficients of known polynomials, their organization within the arrangement known as Pascal's triangle and the properties related to this arrangement. Next, it introduces Arithmetic with the concepts and properties of divisibility and congruence between integers, and then enters into the arithmetic properties of binomial coefficients. Finally, it presents Pascal's triangle modulo p prime, emphasizing the case p=2 and discusses the divisibility of certain expressions with binomials by powers of the prime number p.