Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2017: 0.26

Online
ISSN
1337-2211
See all formats and pricing
More options …
Volume 66, Issue 3

Issues

Diophantine equation X4+Y4 = 2(U4 + V4)

Farzali Izadi / Kamran Nabardi
Published Online: 2016-08-17 | DOI: https://doi.org/10.1515/ms-2015-0157

Abstract

In this paper, the theory of elliptic curves is used for finding the solutions of the quartic Diophantine equation X4+Y4 = 2(U4 + V4).

MSC 2010: Primary 11D45; Secondary 11G05

Key words: Diophantine equation; elliptic curve; congruent number

References

  • [1]

    Brudno, S.: Some new results on equal sums of like powers, Massachusetts Institute of Technology, 1969Google Scholar

  • [2]

    Choudhry, A.: The diophantine equation A4 + 4B4 = C4 + 4D4, Indian J. Pure Appl. Math. 29(11) (1998), 1127–1128.Google Scholar

  • [3]

    Choudhry, A.: On the diophantine equation A4 + hB4 = C4 + hD4, Indian J. Pure Appl. Math. 26(11) (1995), 1057–1061.Google Scholar

  • [4]

    Cohen, H.: Number Theory Volume 1: Tools and Diophantine Equations. Grad. Texts in Math., Springer-Verlag, New York, 2007.Google Scholar

  • [5]

    Elkies, N. D.: On A4 + B4 + C4 = D4, Math. Comp. 51 (1988), 825–835.Google Scholar

  • [6]

    Hardy, G. H.—Wright, E. M.: An Introduction to the Theory of the Numbers (4th ed.), Oxford Univ. Press, London, 1960.Google Scholar

  • [7]

    Koblitz, N.: Introduction to Elliptic Curves and Modular Forms. Grad. Texts in Math., Springer-Verlag, New York, 1984.Google Scholar

  • [8]

    Lander, L. J.: Geometric aspect of diophantine equation involving equal sums of like powers, Amer. Math. Monthly 75 (1968), 1061–1073.Google Scholar

  • [9]

    Richmond, H. W.: On the diophantine equation F = ax4 + by4 + cz4 + dw4 = 0, the product abcd being a square number, J. Lond. Math. Soc. 19 (1944), 193–194.Google Scholar

  • [10]

    Sage Software: Version 4.3.5. http://sagemath.org.

  • [11]

    Silverman, J. H.—Tate, J.: Rational Points on Elliptic Curves. Undergrad. Texts Math., Springer-Verlag, New York, 1992.Google Scholar

  • [12]

    Washington, L. C.: Elliptic Curves: Number Theory and Cryptography (2nd ed.), Taylor § Francis Group, LLC, New Yourk, 2008.Google Scholar

  • [13]

    Zajta, A. J.: Solutions of diophantine equation A4 + B4 = C4 + D4, Math. Comp. 41 (1983), 635–659.Google Scholar

About the article


Received: 2012-11-23

Accepted: 2013-11-07

Published Online: 2016-08-17

Published in Print: 2016-06-01


Citation Information: Mathematica Slovaca, Volume 66, Issue 3, Pages 557–560, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0157.

Export Citation

© 2016 Mathematical Institute Slovak Academy of Sciences.Get Permission

Comments (0)

Please log in or register to comment.
Log in