A246759 Nonnegative numbers k such that x^5 - x^4 + k is reducible.
0, 2, 9, 48, 324, 1280, 3750, 9072, 19208, 36864, 50625, 65610, 82944, 110000, 175692, 269568, 399854, 576240, 810000, 1114112, 1503378, 1994544, 2606420, 3360000, 4278582, 5387888, 6716184, 8294400
Offset: 1
Keywords
Examples
For k=2, x^5 - x^4 + 2 is reducible: x^5 - x^4 + 2 = (x+1) * (x^4 - 2*x^3 + 2*x^2 - 2*x + 2).
Programs
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Mathematica
Select[Range[0,83*10^5],!IrreduciblePolynomialQ[x^5-x^4+#]&] (* Harvey P. Dale, Dec 11 2017 *)
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PARI
for(n=0, 10^7, if( !polisirreducible(x^5-x^4+n), print1(n,", "))); \\ Joerg Arndt, Sep 06 2014
Extensions
More terms from Joerg Arndt, Sep 06 2014
Comments