So for the first part of the question, I have to find the solutions to:
$\ x^2+4x+3=0$ over $\mathbb{Z}_{16}$ I have found these to be $X=5,7,13$ and $15$, just by using standard method to solve a quadratic over a field. However the next part of the question is to find
$\ x^{128}+4x+3=0$ over $\mathbb{Z}_{127}$ How would I go about solving this?
Hint For the first question : Use $x^2+4x+3=(x+1)(x+3)$
Hint for the second question : In $Z_{127}$ you have $x^{127}=x$ for all $x$