The polynomial F_p(x) = x^{2p} + 2x^p + 2 is monogenic if and only if p is not a Wieferich prime.
Chen, Elementary characterization for Galois groups of x^ 12 +ax^6+b
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The paper determines all abelian monogenic trinomials x^{2n} + a x^n + b for integers n ≥ 1, a, b with ab ≠ 0.
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Wieferich Primes and Monogenic Trinomials
The polynomial F_p(x) = x^{2p} + 2x^p + 2 is monogenic if and only if p is not a Wieferich prime.
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A Note on Abelian Monogenic Trinomials
The paper determines all abelian monogenic trinomials x^{2n} + a x^n + b for integers n ≥ 1, a, b with ab ≠ 0.