Geodesic
A note on a conjecture of Jeśmanowicz
Colloquium Mathematicum, Tome 86 (2000) no. 1, pp. 25-30.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let a, b, c be relatively prime positive integers such that $a^2+b^2=c^2$. Jeśmanowicz conjectured in 1956 that for any given positive integer n the only solution of $(an)^x+(bn)^y=(cn)^z$ in positive integers is x=y=z=2. If n=1, then, equivalently, the equation $(u^2-v^2)^x+(2uv)^y=(u^2+v^2)^z$, for integers u>v>0, has only the solution x=y=z=2. We prove that this is the case when one of u, v has no prime factor of the form 4l+1 and certain congruence and inequality conditions on u, v are satisfied.
DOI : 10.4064/cm-86-1-25-30

Moujie Deng 1 ; G. Cohen 1

1 
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Moujie Deng; G. Cohen. A note on a conjecture of Jeśmanowicz. Colloquium Mathematicum, Tome 86 (2000) no. 1, pp. 25-30. doi : 10.4064/cm-86-1-25-30. http://geodesic.mathdoc.fr/articles/10.4064/cm-86-1-25-30/

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