Geodesic
Jeśmanowicz’ Conjecture with Congruence Relations. II
Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 495-505

Voir la notice de l'article provenant de la source Cambridge

DOI

Let $a$ , $b$ , and $c$ be primitive Pythagorean numbers such that ${{a}^{2}}\,+\,{{b}^{2}}\,=\,{{c}^{2}}$ with $b$ even. In this paper, we show that if ${{b}_{0}}\,\equiv \,\in \,\,\,\left( \bmod \,a \right)$ with $\text{ }\!\!\varepsilon\!\!\text{ }\,\in \,\left\{ \pm 1 \right\}$ for certain positive divisors ${{b}_{0}}$ of $b$ , then the Diophantine equation ${{a}^{x}}\,+\,{{b}^{y}}\,=\,{{c}^{z}}$ has only the positive solution $\left( x,\,y,\,z \right)\,=\,\left( 2,\,2,\,2 \right)$ .
DOI : 10.4153/CMB-2014-020-0
Mots-clés : 11D61, 11D09, exponential Diophantine equations, Pythagorean triples, Pell equations 
Fujita, Yasutsugu; Miyazaki, Takafumi. Jeśmanowicz’ Conjecture with Congruence Relations. II. Canadian mathematical bulletin, Tome 57 (2014) no. 3, pp. 495-505. doi: 10.4153/CMB-2014-020-0
@article{10_4153_CMB_2014_020_0,
     author = {Fujita, Yasutsugu and Miyazaki, Takafumi},
     title = {Je\'smanowicz{\textquoteright} {Conjecture} with {Congruence} {Relations.} {II}},
     journal = {Canadian mathematical bulletin},
     pages = {495--505},
     year = {2014},
     volume = {57},
     number = {3},
     doi = {10.4153/CMB-2014-020-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-020-0/}
}
TY  - JOUR
AU  - Fujita, Yasutsugu
AU  - Miyazaki, Takafumi
TI  - Jeśmanowicz’ Conjecture with Congruence Relations. II
JO  - Canadian mathematical bulletin
PY  - 2014
SP  - 495
EP  - 505
VL  - 57
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-020-0/
DO  - 10.4153/CMB-2014-020-0
ID  - 10_4153_CMB_2014_020_0
ER  - 
%0 Journal Article
%A Fujita, Yasutsugu
%A Miyazaki, Takafumi
%T Jeśmanowicz’ Conjecture with Congruence Relations. II
%J Canadian mathematical bulletin
%D 2014
%P 495-505
%V 57
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-020-0/
%R 10.4153/CMB-2014-020-0
%F 10_4153_CMB_2014_020_0

Cité par Sources :