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If p-1 is a factor of p⁴ + p² + p − k solve for k
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If p-1 is a factor of p⁴ + p² + p − k solve for k

User Raatje
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p-1=p^4+p^2+p-k


-1=p^4+p^2-k


\boxed{k=p^4+p^2+1}\Longrightarrow\boxed{p\in\mathbb{R}}

User Kajman
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