ResumeJadrijevic. 62KB Jun 04 2011 12:07:06 AM

Journal de Th´

eorie des Nombres

de Bordeaux

17

_{(2005), 161–167}

On two-parametric family of quartic Thue

equations

par

Borka JADRIJEVI ´

C

R´esum´e. _{Nous montrons que pour tous les entiersmetn, il n’y} a pas de solution non triviale de l’´equation de Thue

x4−2mnx3y+ 2 m2−n2+ 1x2y2+ 2mnxy3+y4= 1, satisfaisant la condition suppl´ementaire pgcd(xy, mn) = 1.

Abstract. _{We show that for all integers m andn there are no} non-trivial solutions of Thue equation

x4−2mnx 3

y+ 2 m2−n 2

+ 1

x2y2+ 2mnxy3+y4= 1, satisfying the additional condition gcd(xy, mn) = 1.

BorkaJadrijevi´c

FESB, University of Split R. Boˇskovi´ca bb

21000 Split, Croatia