

A135842


Prime numbers p of the form 10k+1 for which the quintic polynomial x^5x1 modulus p is factorizable into five binomials.


6



5101, 8161, 9631, 17921, 26681, 31091, 39161, 39671, 40151, 41491, 43331, 44171, 44221, 48541, 75821, 77951, 84391, 94531, 109391, 111521, 113891, 114661, 117511, 118081, 124121, 132241, 141241, 144511, 156371, 160231, 161771, 167381, 174481, 178951, 184321, 184511, 186871, 187091, 204301
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OFFSET

1,1


COMMENTS

According to class field theory each quintic polynomial is completely reducible mod some prime number p of the form 10k+1.


REFERENCES

S. Kobayashi & H. Nakagawa, Resolution of Solvable Quintic Equation, Math. Japonica Vol. 87, No 5 (1992), pp. 883886.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000


MATHEMATICA

a = {}; Do[If[PrimeQ[10n + 1], poly = PolynomialMod[x^5  x  1, 10n + 1]; c = FactorList[poly, Modulus > 10n + 1]; If[Sum[c[[m]][[2]], {m, 1, Length[c]}] == 6, AppendTo[a, 10n + 1]]], {n, 1, 10000}]; a


CROSSREFS

Cf. A135843.
Sequence in context: A260069 A252143 A223400 * A224492 A330730 A219329
Adjacent sequences: A135839 A135840 A135841 * A135843 A135844 A135845


KEYWORD

nonn


AUTHOR

Artur Jasinski, Dec 01 2007


EXTENSIONS

Terms a(19) and beyond from G. C. Greubel, Dec 06 2016


STATUS

approved



