方程Π_P Φ_3(P) = Π_P P^2 / F_2[x]

Gulf Journal of Mathematics Pub Date : 2022-03-15 DOI:10.56947/gjom.v12i2.722

L. Gallardo

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引用次数: 1

摘要

我们研究1937年Steuerwald解决的一个算术问题的多项式变体。更确切地说，我们在一个温和的条件下证明了题目上的方程不存在解a:= ΠP P2∈F2[x]，且P不可约，且ω(a) < 16。我们无条件地证明了deg(P)≥40。这在已知结果的基础上进行了改进。

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On the equation Π_P Φ_3(P) = Π_P P^2 over F_2[x]

We work a polynomial variant of an arithmetic problem solved by Steuerwald in 1937. More precisely, we prove, under a mild condition, that the equation on the title, has no solutions A := ΠP P2 ∈ F2[x], with irreducible P, and ω(A) < 16. Unconditionally, we prove that deg(P) ≥ 40. This improves on known results.

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Gulf Journal of Mathematics

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