A bound for the solutions of the Diophantine equation $D_1 x^2 + D_2^m = 4y^n$

Mihai Cipu

doi:10.3792/pjaa.78.179

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Dec. 2002 A bound for the solutions of the Diophantine equation $D_1 x^2 + D_2^m = 4y^n$

Mihai Cipu

Proc. Japan Acad. Ser. A Math. Sci. 78(10): 179-180 (Dec. 2002). DOI: 10.3792/pjaa.78.179

Abstract

We show that in every solutions $(D_1,D_2,x,y,m,n)$ of the equation $D_1 x^2 + D_2^m = 4 y^n$ with $n$ prime and coprime with the class-number of the imaginary quadratic field $\mathbf{Q}(\sqrt{-D_1D_2})$ one has $n \leq 5351$.

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Mihai Cipu. "A bound for the solutions of the Diophantine equation $D_1 x^2 + D_2^m = 4y^n$." Proc. Japan Acad. Ser. A Math. Sci. 78 (10) 179 - 180, Dec. 2002. https://doi.org/10.3792/pjaa.78.179