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On the diophantine equation \((x^m+1)(x^n+1)=y^2\). (English) Zbl 0893.11013

The author proves that if \(x,y,m,n\) are natural numbers such that \(x<1\), \(n> m\),
and \((x^m+1)\) \((x^n+1) =y^2\), then \((x,y,m,n) =(7,20,1,2)\). The proof makes use of prior results regarding Pell numbers, related diophantine equations, and linear forms in two logarithms.

MSC:

11D61 Exponential Diophantine equations
11J86 Linear forms in logarithms; Baker’s method
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