On a conjecture on Pythagorean numbers (Q1318925)
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scientific article; zbMATH DE number 549026
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a conjecture on Pythagorean numbers |
scientific article; zbMATH DE number 549026 |
Statements
On a conjecture on Pythagorean numbers (English)
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29 September 1994
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L. Jésmanowicz conjectured that if \(u\), \(v\), \(w\) are Pythagorean numbers, then the diophantine equation on \(\ell,m,n\in\mathbb{N}\) \[ u^ \ell+ v^ m= w^ n \] has the unique solution \((\ell,m,n)= (2,2,2)\). In this paper, the authors prove this conjecture in some special cases.
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quadratic diophantine equation
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Pythagorean numbers
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