*Article* **Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method**

**Mercedes Orús-Lacort 1,2 and Christophe Jouis 3,4,\***


**Abstract:** In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in analyzing the sequence generated by odd numbers, we can deduce a formula for the general term of the Collatz sequence for any odd natural number *n* after several iterations. This formula is used in one case that we analyze using the mathematical complete induction method in the process of demonstrating the conjecture.

**Keywords:** number theory; Collatz conjecture

**MSC:** 11-02
