Solving binomial Thue equations

We consider binomial Thue equations of type $x^n-m{y}^n=\pm 1$ in $x,y\in Z$. Optimizing the method of Peth\H o we perform an extensive calculation by a high performance computer to determine all solutions with $\max (\mathrm{\mid }x\mathrm{\mid },\mathrm{\mid }y\mathrm{\mid })<{10}^{500}$ of binomial Thue equations for $m<{10}^7$ for exponents $n=3,4,5,7,11,13,17,19,23,29$.