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 University Press

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
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