(In reply to
Answer only (possible spoiler) by broll)
So annoying to get an integer answer without an explanation!
However, there is a similar problem, with x^{3}  x  1 = 0, leading to a wellknown sequence.
Now for x^{3}  x  1 = 0, the roots are: x~~1.3247,x~~0.662360.56228i, x~~0.66236+0.56228i,
while for x^{3}  x + 1 = 0, the roots are:
x~~1.3247, x~~0.662360.56228i, x~~0.66236+0.56228i, so there's just a sign change in the real part.
Since we are raising to an even power, the result is the same for either equation, see:
http://mathworld.wolfram.com/PerrinSequence.html
http://en.wikipedia.org/wiki/Perrin_number

Posted by broll
on 20150207 04:22:17 