Geodesic
The Diophantine equation $(bn)^{x}+(2n)^{y}=((b+2)n)^{z}$
Min Tang 1   ; Quan-Hui Yang 2
1 Department of Mathematics Anhui Normal University Wuhu 241003, China
2 School of Mathematical Sciences Nanjing Normal University Nanjing 210023, China
Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 95-100 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Recently, Miyazaki and Togbé proved that for any fixed odd integer $b\geq 5$ with $b\not =89$, the Diophantine equation $b^{x}+2^{y}=(b+2)^{z}$ has only the solution $(x,y,z)=(1,1,1)$. We give an extension of this result.
DOI : 10.4064/cm132-1-7
Mots-clés : recently miyazaki togb proved fixed odd integer geq diophantine equation has only solution extension result

Min Tang  1   ; Quan-Hui Yang  2

1 Department of Mathematics Anhui Normal University Wuhu 241003, China
2 School of Mathematical Sciences Nanjing Normal University Nanjing 210023, China 
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Min Tang; Quan-Hui Yang. The Diophantine equation $(bn)^{x}+(2n)^{y}=((b+2)n)^{z}$. Colloquium Mathematicum, Tome 132 (2013) no. 1, pp. 95-100. doi: 10.4064/cm132-1-7

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