On the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\). (Q1812479)
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scientific article; zbMATH DE number 1930960
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\). |
scientific article; zbMATH DE number 1930960 |
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On the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\). (English)
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19 February 2004
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The author gives upper bounds for the solution \(l\) of the equation \({n\choose 2}= cx^l\) and \({n\choose 3}= cx^l\), where \(n\), \(c\), \(l\) are nonzero integers, by using results concerning the equation \(ax^l- by^l= c\) with \(a\), \(b\), \(c\) nonzero integers. These solutions are also determined in some special cases.
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Thue equations
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elliptic curves
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