Does anyone know of any papers dealing with the resultant of a binomial $x^n+a$ and a trinomial $x^r+bx^s+c$ ?
Even special cases would be of interest.
(The resultant of two binomials is well known.)
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1$\begingroup$ Any reference for the "well-known" result? $\endgroup$– Igor RivinCommented Feb 15, 2018 at 19:33
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1$\begingroup$ related: mathoverflow.net/questions/59859/… $\endgroup$– Abdelmalek AbdesselamCommented Feb 15, 2018 at 20:17
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$\begingroup$ Apologies. See Lemma 3 in the 1962 paper "Factorization of Polynomials over Finite Fields" by Richard Swan msp.org/pjm/1962/12-3/pjm-v12-n3-p27-p.pdf $\endgroup$– Gary McGuireCommented Feb 15, 2018 at 20:37
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$\begingroup$ Crossposted also at Math.SE. $\endgroup$– Jyrki LahtonenCommented Feb 16, 2018 at 22:09
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1$\begingroup$ I did some calculations: For the special case $r=2, s =1, b=-1, c=-1$ (i.e. the fibonacci quadratic polynomial) one gets $\mathrm{Res}(x^n +a, x^2-x-1)=a^2 + \mathrm{Lucas}(n) \cdot a +(-1)^n$, with $(\mathrm{Lucas}(n)) = (1,3,4,7,\ldots)$. Should not be too difficult to prove and could be a starting point for more general cases. $\endgroup$– Andreas RüdingerCommented Feb 17, 2018 at 11:21
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