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In this article, we determine all abelian monogenic trinomials of the form $x^{2n}+ax^{n}+b$, where $n,a,b\\in {\\mathbb Z}$ with $n\\ge 1$ and $ab\\ne 0$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.25753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-25T12:04:28Z","cross_cats_sorted":[],"title_canon_sha256":"0a2f7861c8beba2b80234eead8458a10827af77cb4d220ef3dab5a23e997ec21","abstract_canon_sha256":"2c11ec8cb624fd25d133020df484e5d3785e6d67ede4835ec8d3527f9c463974"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T02:04:53.354750Z","signature_b64":"MBiqt/LW5vh3LUfE3TlI8Guz2/JWK21NHUniKdvQy5d1NHuDF7F2RFLfHvRjsg6kgOBTZr4Fac5HGzwnMwt0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4bca2f1e97d2f664364b80d24ad84db05111113989d8ff78961b151913374b5","last_reissued_at":"2026-05-26T02:04:53.353981Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T02:04:53.353981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Abelian Monogenic Trinomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Lenny Jones","submitted_at":"2026-05-25T12:04:28Z","abstract_excerpt":"An abelian monogenic polynomial $f(x)\\in {\\mathbb Z}[x]$ is a monic polynomial of degree $N$ that is irreducible over ${\\mathbb Q}$, such that the Galois group of $f(x)$ over ${\\mathbb Q}$ is abelian, and $\\{1,\\theta,\\theta^2,\\ldots,\\theta^{N-1}\\}$ is a basis for the ring of integers of ${\\mathbb Q}(\\theta)$, where $f(\\theta)=0$. 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