Every Remainder Everywhere

The paper Every Remainder Everywhere.pdf shows that: For every modulus N ≥ 1, every w not divisible by 3, every residue r and every bound B, there is n > B with n ≡ r (mod N) whose Collatz trajectory reaches w. The proof is formalized in Lean 4 in a single file, with no imports. ERE.lean SHA-256: a34df33236a71519340dfbf4d9193a95fa77a64652a8a3bdbef6f2878360f51a

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23757321
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Every Remainder Everywhere

André Hallqvist
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Every Remainder Everywhere

André Hallqvist
preprint en

Abstract

The paper Every Remainder Everywhere.pdf shows that: For every modulus N ≥ 1, every w not divisible by 3, every residue r and every bound B, there is n > B with n ≡ r (mod N) whose Collatz trajectory reaches w. The proof is formalized in Lean 4 in a single file, with no imports. ERE.lean SHA-256: a34df33236a71519340dfbf4d9193a95fa77a64652a8a3bdbef6f2878360f51a

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Every Remainder Everywhere — André Hallqvist · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS