On the family of Diophantine triples \(\{k+1,4k,9k+3\}\) (Q1046810)
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scientific article; zbMATH DE number 5651911
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the family of Diophantine triples \(\{k+1,4k,9k+3\}\) |
scientific article; zbMATH DE number 5651911 |
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On the family of Diophantine triples \(\{k+1,4k,9k+3\}\) (English)
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29 December 2009
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The paper provides an extendibility result concerning a parametric family of Diophantine triples. The authors prove that if \(k\) and \(d\) are positive integers such that the product of any two distinct elements of the set \(\{k+1,4k,9k+3,d\}\) increased by \(1\) is a perfect square, then \(d=144k^3+192k^2+76k+8\).
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Diophantine \(m\)-tuple
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Pell equation
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Diophantine approximation
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linear forms in logarithms
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