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On a conjecture on Pythagorean numbers. (English) Zbl 0796.11009

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.
Reviewer: Ke Zhao (Chengdu)

MSC:

11D09 Quadratic and bilinear Diophantine equations

Citations:

Zbl 0796.11010
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References:

[1] L. Jesmanowicz: Kilka uwag o liczbach pitagorejwkich (Some remarks on Pythagorean numbers). Wiadom. Mat, 1, 196-202 (1956). · Zbl 0074.27205
[2] N. Terai: The diophantine equation x2 + qm = pn. Acat Arith., LXIII.4, 351-358 (1993). · Zbl 0770.11020
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