  Casually introduced thirty years ago, a simple algebraic equation of degree
4, with coefficients in Fp[T], has a solution in the field of power series in
1/T, over the finite field Fp. For each prime p > 3, the continued fraction
expansion of this solution is remarkable and it has a different general pattern
according to the remainder, 1 or 2, in the division of p by 3. We describe two
very large families of algebraic continued fractions, each containing these
solutions, according to the class of p modulo 3. We can compute the
irrationality measure for these algebraic continued fractions and, as a
consequence, we obtain two different values for the solution of the quartic
equation, only depending on the class of p modulo 3.
