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On the equation $a^2 + b^{2p} = c^5$

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Chen I.

Acta Arithmetica

2010

tom 143

nr 4

345-375

On the equation a³ + b³ⁿ = c²

58%

Bennett M., Chen I., Dahmen S., Yazdani S.

Acta Arithmetica

2014

tom 163

nr 4

327-343

We study coprime integer solutions to the equation a³ + b³ⁿ = c² using Galois representations and modular forms. This case represents perhaps the last natural family of generalized Fermat equations descended from spherical cases which is amenable to resolution using the so-called modular method. Our techniques involve an elaborate combination of ingredients, ranging from ℚ-curves and a delicate multi-Frey approach, to appeal to intricate image of inertia arguments.

Ograniczanie wyników

2 Acta Arithmetica

2 Chen I.

1 Bennett M.

1 Dahmen S.

1 Yazdani S.

1 2014

1 2010

Wyniki wyszukiwania

On the equation $a^2 + b^{2p} = c^5$

On the equation a³ + b³ⁿ = c²