reg>http://www.math.harvard.edu/~elkies/trinomial.html <http://www.math.harvard.edu/%7Eelkies/trinomial.html> gives a (rational) continuum of irreducible, supposedly solvable sextics: (125 - u)*x^6 + 12*u*(u + 3)^2*x + u*(u - 5)*(u + 3)^2 but my sextic solver fails for u≠0. (≠-3,≠5) Can anybody propose a correction? CG>I have no correction, but I concur with your result. For example, with u = 4 I get 121x^6 + 2352x - 196 with Galois group PSL(2,5): polgalois(121*x^6 + 2352*x - 196) %1 = [60, 1, 1, "L(6) = PSL(2,5) = A_5(6)"] which is not solvable. Charles Greathouse Analyst/Programmer Case Western Reserve University Mea gufa. With more patience than I deserve, Elkies privately explained that his paper claims only that the Galois groups are atypically small, not necessarily small enough to solve. He also had no news re the possibility of a solvable, irreducible septic trinomial. Come to think of it, I don't even recall seeing a solvable, irreducible x^6+ax+b. --rwg