On a diophantine equation \((x^2 - 1)(y^2 - 1) = (z^2 - 1)^2\) (Q912891)
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scientific article; zbMATH DE number 4145998
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a diophantine equation \((x^2 - 1)(y^2 - 1) = (z^2 - 1)^2\) |
scientific article; zbMATH DE number 4145998 |
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On a diophantine equation \((x^2 - 1)(y^2 - 1) = (z^2 - 1)^2\) (English)
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1987
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All integer solutions \((x,y,z)\) of this equation with \(z = (x-y)/2\) have been determined by \textit{A. Schinzel} and \textit{W. Sierpiński} [Elem. Math. 18, 132--133 (1963; Zbl 0126.073)]. Other solutions are \((x,y,z) = (4,31,11)\), \((2,97,13)\), \((155,48049,2729)\). The author arrives at these solutions by a method involving Pell's equation.
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quartic diophantine equation
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Pell's equation
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