[GAP Forum] help with solving equations on finite fields..

[maycon carneiro]

Hi all, i'm new in the GAP and i really need help.. my problem is:

I creat an AlgebraicExtension over GF(2) using the polynomial x^3+x^2+1,

gap>z2:=GF(2);
x:=X(z2,"x");
pol:=x^3+x^2+1;
F8:=AlgebraicExtension(z2,pol);
a:=RootOfDefiningPolynomial(F8);

now, i'd like to get the solutions over F8 of the equation:

z^2+z*y+a*y^2= c, where c is an especified element of F8, say a^2.. and z,
y are variables in F8

how can i do this? or at least in one variable, say z, and i'll put an
especified element for y..

can someone help me?
Thanks..

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