Authors and affiliations
In this note, we study the diagonal nonhomogeneous symmetric Diophantine equation of the title, and show that when a solution has been found, a series of other solutions can be derived. This shows that difference of quintics equals difference of cubics for infinitely many integers. We do so using a method involving elliptic curves, which makes it possible to naturally find any solution in a matter of minutes.
- Diophantine equation
- Elliptic curve
- Bremner, A., Bremner, A., M. Ulas, On xa ± yb ± zc ± wd =0, 1/a+1/b+1/c+1/d=1, Int. J. Number Theory, Vol. 7, 2011, 2081–2090
- Choudhry, A, Symmetric Diophantine equations, Rocky Mountain J. Math. , Vol. 34, 2004, 1281–1298.
- Dickson, L. E., History of the Theory of Numbers II, Chelsea Publishing Company, New York, 1920.
- Sage software, Version 4.5.3, http://www.sagemath.org
- Washington, L. C., Elliptic Curves: Number Theory and Cryptography, 2nd ed., CRC Press, Taylor & Francis Group, Boca Raton, FL, 2008.
Cite this paper
Izadi, F. & A. S. Zargar. (2014). On integer solutions of A5 + B3 = C5 + D3 Notes on Number Theory and Discrete Mathematics, 20(5), 20-24.