Hi,
I have two questions.


1. Show that x^5+x^2+1=0 has four imaginary roots


2.Show that fermat's little theorem is a special case of Euler's theorem .


Thanks,

Chaand

#1: http://en.wikipedia.org/wiki/Fermat's_little_theorem

#2: f(x)=x^{5}+x^{2}+1

f(-x)=-x^{5}+x^{2}+1

Notice, by Descartes' rule of signs, the number of zeros of f(x) either is equal to the number of variations of sign of f(-x) or is less than that by an even integer.

Therefore, you have 1 negative root and 4 complex roots.