This article is cited in 2 papers

Binomial Thue equations, ternary equations, and power values of polynomials

K. Gyȍry, Á. Pintér

Institute of Mathematics, University of Debrecen, Hungary

Abstract: We explicitly solve the equation $Ax^n-By^n=\pm1$ and, along the way, we obtain new results for a collection of equations $Ax^n-By^n=z^m$ with $m\in\{3,n\}$, where $x,y,z,A,B$, and $n$ are unknown nonzero integers such that $n\geq3$, $AB=p^\alpha q^\beta$ with nonnegative integers $\alpha$ and $\beta$ and with primes $2\leq p<q<30$. The proofs require a combination of several powerful methods, including the modular approach, recent lower bounds for linear forms in logarithms, somewhat involved local considerations, and computational techniques for solving Thue equations of low degree.

UDC: 511.52

 English version: Journal of Mathematical Sciences (New York), 2012, 180:5, 569–580

Bibliographic databases:

• 
•