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In this article, we show that ${\\mathcal F}_p(x):=x^{2p}+2x^{p}+2$ is monogenic if and only if $p$ is not a Wieferich prime.","authors_text":"Lenny Jones","cross_cats":[],"headline":"The trinomial x^{2p} + 2x^p + 2 is monogenic if and only if the prime p is not Wieferich.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-05-13T12:52:46Z","title":"Wieferich Primes and Monogenic Trinomials"},"references":{"count":72,"internal_anchors":0,"resolved_work":72,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Cohen, A Course in Computational Algebraic Number Theory, Springer-Verlag , 2000","work_id":"18906986-5d90-4d2f-a55e-c24246f72c28","year":2000},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"J. Harrington and L. Jones, A note on generalised Wall-Sun-Sun primes , Bull. Aust. Math. 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