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On the equation \(ax^n-by^n=c\). (English) Zbl 0498.10014
The author proves some theorems on the upper bounds for the number of integral solutions to the title equation and similar equations. The results are obtained in terms of the number \(R(n,c)\) of residue classes \(z\pmod c\) satisfying the congruence \(z^n\equiv 1\pmod c\).

MSC:
11D41 Higher degree equations; Fermat’s equation
11D45 Counting solutions of Diophantine equations
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References:
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