%0 Journal Article
%T Trinomials ax8+bx+c with Galois groups of order 1344
%A Tengely
%A Szabolcs
%J -
%D 2018
%R 10.3336/gm.53.2.04
%X Sa£¿etak Bruin and Elkies ([7]) obtained the curve of genus 2 parametrizing trinomials ax8 + bx + c whose Galois group is contained in G1344 = (£¿/2)3 £¿ G168. They found some rational points of small height and computed the associated trinomials. They conjecture that the only £¿-rational points of the hyperelliptic curve Y2 = 2X6 + 28X5 + 196X4 + 784X3 + 1715X2 + 2058X + 2401 are given by (X, Y ) = (0, ¡À 49), (-1, ¡À 38), (-3, ¡À 32), and (-7, ¡À 196). In this paper we prove that the above points are the only S-integral points with S={2,3,5,7,11,13,17,19}
%K Trinomials
%K hyperelliptic curves
%K S-integral points
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=313465