Relacionando critérios de divisibilidades com sistemas de numeração

In this work we are going to relate the divisibility of a number to its numbering system on a given basis. More precisely, we determine when a number written on a given base r is divisible by ( r – 1 ) and ( r + 1 ) . We started from this generalization and obtained the well-known divisibility criteria for 9 and 11, when the number in question is written in the base r = 10. We use these concepts to solve math olympics exercises, graduate questions and unveil some common games in the circles of friends that, the secret answers, are directly linked to numbering systems.