Solutions of a class of quartic Thue inequalities

Let n>1n>1 be an integer. In this paper, first we show that the quartic Thue equality x4−(n+1)x3y−nx2y2+2xy3+y4=μx4−(n+1)x3y−nx2y2+2xy3+y4=μ can be transformed into a system of Pellian equations by the Tzanakis method if and only if n=c2+c−5n=c2+c−5, for some integer c≥3c≥3. We determine all positive integer solutions (x,y)(x,y) with 0<∣μ∣≤c+20<∣μ∣≤c+2.