{
  "annotation_id": "c4a7418c-e3b9-428a-9802-4cd4c8683a85",
  "date_created": "2026-02-17T05:53:07.519000Z",
  "date_modified": "2026-02-17T05:53:07.519000Z",
  "file_hash": "192ebd1a94215d2dce8ca88df7218857b8f7ac17e9bf5f5943b2130ed6a5acad",
  "private": false,
  "record": {
    "abstract": "In this paper, we will introduce an extension to the Collatz\u0027s 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,\n  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 $10$.",
    "arxiv_id": "2601.06208",
    "authors": [
      "Abderrahman Bouhamidi"
    ],
    "categories": [
      "math.GM"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "An Extension of the Collatz Conjecture modulo $2^p+2^q$",
    "url": "https://arxiv.org/abs/2601.06208",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b992d84e-d811-43b1-9f91-eec65e4f54ce",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}