Let $$f_{a,b}(x)=x^3+(u-1-a-b)x^2+ax+b.$$ where $$u\in\mathbb{Z}_p^*$$ is fixed . Let $$S$$ be the set consisting of all pairs $$(a,b)\in\mathbb{Z}_p^2$$ such that $$f_{a,b}(x)$$ factor linearly.Then what is the cardinality of S?
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Cubic polynomial over z_p
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