Bulletin of the Belgian Mathematical Society - Simon Stevin

Modular congruences, Q-curves, and the diophantine equation $x^4 + y^4 = z^p $

Luis V. Dieulefait

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Abstract

We prove two results concerning the generalized Fermat equation $x^4 + y^4 = z^p$. In particular we prove that the First Case is true if $p \neq 7$

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 12, Number 3 (2005), 363-369.

Dates
First available in Project Euclid: 8 September 2005

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1126195341

Digital Object Identifier
doi:10.36045/bbms/1126195341

Mathematical Reviews number (MathSciNet)
MR2173699

Zentralblatt MATH identifier
1168.11010

Subjects
Primary: 11D41: Higher degree equations; Fermat's equation 11F11: Holomorphic modular forms of integral weight

Keywords
diophantine equations elliptic curves modular forms

Citation

Dieulefait, Luis V. Modular congruences, Q-curves, and the diophantine equation $x^4 + y^4 = z^p $. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), no. 3, 363--369. doi:10.36045/bbms/1126195341. https://projecteuclid.org/euclid.bbms/1126195341


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