# ag.algebraic geometry – Under what circumstances is the polynomial of diploma \$6\$ irreducible? retort

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## ag.algebraic geometry – Under what circumstances is the polynomial of diploma \$6\$ irreducible?

Let $$ok$$ breathe a consummate bailiwick of attribute $$p neq 2,3$$ such that $$omega := sqrt[3]{1} in ok$$, the place $$omega neq 1$$. assume a fully irreducible (not essentially homogenous) quadratic polynomial $$Q in ok[s_1, s_2]$$ in two variables $$s_1, s_2$$. Under what circumstances is the polynomial $$Q^prime(t_1,t_2) := Q(t_1^3, t_2^3)$$ (of diploma $$6$$) completely irreducible (or not less than irreducible over $$ok$$) ?

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