DIVISIBILITY CRITERIA FOR LARGE NUMBERS
Divisibility. Prime Numbers. Divisibility Theorem. Applications to Teaching.
In this work, results related to division in integers will be presented, in view of the need to determine if a number n, is divisible by p, from the combination of the digits of n, to n, p ∈ Z. Throughout the chapters, we present elementary notions about sets, finite induction, divisibility and prime numbers so that it is possible to develop tools capable of enabling the demonstration of the theorem that allows us to achieve the objective of this work. The result we seek to prove is titled as Divisibility Theorem, which we will apply to basic education through the Divisibility Criteria using many digits at a time and as applications to higher education, we present the demonstration of Arithmetic results.