An Extension of the Collatz Conjecture modulo $2^p+2^q$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915719696875520 |
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| author | Bouhamidi, Abderrahman |
| author_facet | Bouhamidi, Abderrahman |
| contents | In this paper, we will introduce an extension to the Collatz's conjecture. This conjecture may be seen as a general conjecture that unifies the Collatz one together with many other similar conjectures. For instance, we propose our new conjecture modulo $10$ which may be stated as follows. Starting from any positive integer,
if it is a multiple of $10$ then divide it by 10, otherwise, multiply it by $12$, add $8$ times its last digit and divide the result by $10$. Repeat the process infinitely. Regardless the starting number, the process eventually reaches $4$ after a finite number of iterations. The genaral conjecture studied here will encompasse the classical Collatz conjecture togher with our proposed one modulo $10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06208 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An Extension of the Collatz Conjecture modulo $2^p+2^q$ Bouhamidi, Abderrahman General Mathematics In this paper, we will introduce an extension to the Collatz's conjecture. This conjecture may be seen as a general conjecture that unifies the Collatz one together with many other similar conjectures. For instance, we propose our new conjecture modulo $10$ which may be stated as follows. Starting from any positive integer, if it is a multiple of $10$ then divide it by 10, otherwise, multiply it by $12$, add $8$ times its last digit and divide the result by $10$. Repeat the process infinitely. Regardless the starting number, the process eventually reaches $4$ after a finite number of iterations. The genaral conjecture studied here will encompasse the classical Collatz conjecture togher with our proposed one modulo $10$. |
| title | An Extension of the Collatz Conjecture modulo $2^p+2^q$ |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2601.06208 |