OFFSET
1,1
COMMENTS
This polynomial factors iff p == 1 mod 4, but the positivity behavior seems restricted to p == 5 mod 8 with 149 as the first exception.
EXAMPLE
For p=5 we have 625x^8+125x^6+25x^4+5x^2+1=(25x^4+25x^3+15x^2+5x+1)(25x^4-25x^3+15x^2-5x+1)
PROG
(PARI) posipoly(pol) = {for (i=1, poldegree(pol), if (polcoeff(pol, i) <0, return(0)); ); return (1); }
lista(n) = {forprime(p=3, n, fp = factor(sum(i=0, p-1, p^i*x^(2*i))); if (matsize(fp) == [2, 2], if (posipoly(fp[2, 1]) || posipoly(fp[1, 1]), print1(p, ", ")); ); ); } \\ Michel Marcus, Apr 14 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Aart Blokhuis (aartb(AT)win.tue.nl), Dec 09 2002
EXTENSIONS
Corrected and extended by Michel Marcus, Apr 14 2013
Added more terms, Joerg Arndt, Apr 19 2013
STATUS
approved