We consider the parametric family of sextic Thue equations x6−2mx5y−5(m+3)x4y2−20x3y3+5mx2y4+2(m+3)xy5+y6=λ where
m∈Z is an integer and λ is a divisor of 27(m2+3m+9). We
show that the only solutions to the equations are the trivial ones with
xy(x+y)(x−y)(x+2y)(2x+y)=0.Comment: 12 pages, 2 table