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Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method

Author

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  • Mercedes Orús-Lacort

    (College Mathematics, Universitat Oberta de Catalunya, Rambla del Poblenou 156, 08018 Barcelona, Spain
    College Mathematics, Universidad Nacional de Educación a Distancia, Calle Pintor Sorolla 21, 46002 Valencia, Spain)

  • Christophe Jouis

    (Département Langues Etrangères Appliquées (LEA), Université de la Sorbonne Nouvelle Paris 3, 75005 Paris, France
    Centre d’Analyse et de Mathématique Sociales—CAMS, 75006 Paris, France)

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.

Suggested Citation

  • Mercedes Orús-Lacort & Christophe Jouis, 2022. "Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method," Mathematics, MDPI, vol. 10(12), pages 1-7, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1972-:d:833730
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    Cited by:

    1. Xiang Li & Shuo Zhang & Wei Zhang, 2023. "Applied Computing and Artificial Intelligence," Mathematics, MDPI, vol. 11(10), pages 1-4, May.

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    Keywords

    number theory; Collatz conjecture;

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