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Our method consists in relating a solution (a,b,c) to the previous equation to a solution (a,b,c_1) of another Diophantine equation with coefficients in $\\Q(\\sqrt{13})$. We then construct Frey-curves associated with (a,b,c_1) and we prove modularity of them in order to apply the modular approach via Hilbert cusp forms over $\\Q(\\sqrt{13})$. 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