Consider the biquadratic equation, x^4 + x^3+x^2 +x +1 =0 in Z _11
I find that the equation has no solutions from a brute force method of trying all numbers from 1 to 10 for x.
I would like to know if there is another method to actually prove that there is no solution for this equation.
Thanks in advance,
MAX
I can't fault your logic, but I'm getting the solution to to be all numbers x in Z_11! Obviously all of these cannot solve the original equation. I don't see how this gets us anywhere. How do you whittle them down to the solutions to the original problem?
-Dan
Edit: Oh Heavens I'm being silly. I got it. (I hope you aren't responding to this yet.)