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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
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Cite this paperAPA
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.Chicago
Izadi, Farzali, and Arman Shamsi Zargar. “On Integer Solutions of A5 + B3 = C5 + D3.” Notes on Number Theory and Discrete Mathematics 20, no. 5 (2014): 20-24.MLA
Izadi, Farzali, and Arman Shamsi Zargar. “On Integer Solutions of A5 + B3 = C5 + D3.” Notes on Number Theory and Discrete Mathematics 20.5 (2014): 20-24. Print.