This work aims to present some properties of the class of Arithmetic Balanced numbers
and from these results extend to Geometric Balanced numbers, for that, we use notions
and concepts of Combinatorial Analysis emphasizing the following contents Arrangement,
Permutation, Factorial, Permutation with Repetition, Arithmetic and Geometric Means
and the Inequality of Means, we intend to present general results related to the properties,
as well as to enumerate or count for some particular cases using the notion of the Multipli-
cative Principle and the Counting Principles Enabling a more fluid mechanism to obtain
the counting of Arithmetic and Geometric Numbers, and from this conception, present
problems related to fundamental issues in the development of the research, elaborating
during the processes linked to classes of Balanced Numbers, as well as problems of the
respective question banks OBMEP/OBM will be presented that address issues related to
the content presented in preliminary content in order to contribute to the understanding
and development of work-related themes, the proposal is in the field of Problem Solving
Methodology, and it is used as a means of systematizing concepts related to Balanced
numbers , exalting the importance of problematization.
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