Diophantine triplets and the Pell sequence (Q2735221)
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scientific article; zbMATH DE number 1640213
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Diophantine triplets and the Pell sequence |
scientific article; zbMATH DE number 1640213 |
Statements
3 October 2002
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Diophantine triplet
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Diophantine quadruplet
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Fibonacci sequence
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Pell sequence
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0.97785366
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0.96060246
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0.92814976
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0.91033834
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0.90853137
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0.90338784
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0.90020096
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0.8988768
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Diophantine triplets and the Pell sequence (English)
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A Diophantine triplet is a set of three positive integers \((a,b,c)\) such that \(a < b< c\) and \(ab = 1, bc = 1, ac =1\) are integer squares. A diophantine quadruplet is defined in the same way. The aim is to construct several different infinite families of Diophantine triplets using elements of a Pell sequence. Then a general result which gives formulas for a doubly infinite family of Diophantine triples is shown. Finally, an infinite family of Diophantine quadruplets is produced.
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