Is there any general way to find 'one' monic irreducible polynomial of degree $n$? Does there exist any algorithm to find it?
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1$\begingroup$ I'd venture to guess the answer is no. $\endgroup$– Rushabh MehtaNov 8, 2019 at 1:21
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3$\begingroup$ Irreducible over which field? $x^n+2x^{n-1}+\cdots+ 2x+2$ is irreducible over $\mathbb Q$ by Eisenstein's criterion for any $n>0$. $\endgroup$– Randy MarshNov 8, 2019 at 2:00
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$\begingroup$ I can see now that you have the finite-fields tag. In that case, there are algorithms for computing Conway polynomials, e.g. eprints.cs.vt.edu/archive/00000493 and a database at math.rwth-aachen.de/~Frank.Luebeck/data/ConwayPol/… $\endgroup$– Randy MarshNov 8, 2019 at 2:35
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1$\begingroup$ Related. $\endgroup$– Jyrki LahtonenNov 8, 2019 at 10:48
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$\begingroup$ Related 2. $\endgroup$– Jyrki LahtonenNov 8, 2019 at 10:53
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