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Old 2020-04-11, 02:19   #2
carpetpool
 
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"Sam"
Nov 2016

26·5 Posts
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I've been back on researching the task again. I thought I might share some new results, if they are not known already:

x^5 + (n^2 + n + 4)*x^4 + (-2*n^2 - 2*n + 2)*x^3 + (-n^4 - 2*n^3 - 10*n^2 - 9*n - 5)*x^2 + (-3*n^2 - 3*n - 2)*x + n^2 + n + 1

x^7 + (n^3 - 3*n^2 - 4*n - 1)*x^6 + (-3*n^5 + 9*n^3 + 3*n^2 + 3*n - 12)*x^5 + (3*n^7 + 6*n^6 - 4*n^5 + n^4 - 7*n^3 + 28*n^2 + 15*n + 7)*x^4 + (-n^9 - 5*n^8 - 2*n^7 - 5*n^6 + 6*n^5 - 11*n^4 - 21*n^3 + 12*n^2 - n + 28)*x^3 + (n^10 + n^9 + 2*n^8 - n^7 - 9*n^6 + 4*n^5 - 32*n^4 - 6*n^3 - 49*n^2 + 5*n - 14)*x^2 + (-n^9 + 3*n^8 - n^7 + 11*n^6 + 4*n^5 + 4*n^4 - 10*n^3 - 30*n^2 - 20*n - 9)*x - 3*n^7 + 3*n^6 - 7*n^5 + 14*n^4 - 5*n^3 + 12*n^2 - 6*n - 1

As far as I know, there is only one other known cyclic septic besides the one I have listed here.
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