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What can I say about $x^4 \equiv -4 \mod p$ where $p$ is prime? In general what can I do with powers that are greater than $2$ and where I cannot use reciprocity, legendre/jacobi etc... In general what can I say about a quadratic polynomial modulo $p$: For instance $(x-1)^2 \equiv 1 \mod p$

By 'what can I say' I mean $p \equiv$ something $\mod 4$ or $8$

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    I mean $-4$. I just fixed my question.2012-11-02

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$ x^4 + 4 = ((x-1)^2 + 1) ((x+1)^2 + 1) $

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    @CodeKingPlusPlus .2017-01-31