“…It is amusing to note that we encounter the equation 2wA = y2 + 1 considered by Ljunggren [9,14], and its (perhaps unexpected) integer point (w, y) = (13,239). One reason for studying the "simplest fields" is that the roots of the polynomials yield explicit units that often generate subgroups of small index in the full groups of units [2,3,4,5,6,7,10,11,12,13]. In the present situation, since the extensions we obtain are non-Galois and therefore contain few roots, we are forced to consider the Galois closure, in which case we cannot hope to obtain a maximal set of independent units as roots of our polynomials.…”