19 Aug
2005
19 Aug
'05
2:24 p.m.
rwg wrote:
Apropos the cyclotomic discussion, I assume everybody knows about the 2s in factor(x^105-1). What is the lowest degree polynomial with coeffs in {-1,0,1} with a coeff of 2 in its irreducible factorization?
(1-x)(1+2x+x^2+x^3+x^4+...+x^n) will, of course, only have {-1,0,1} coeffs. Irreducibility fails for n=2, but the n=3 example x^4+x^2-x-1 works. (I'll let you dispatch degree 3 by hand yourself :-). --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.