Abstract
In Chapter 3, we found a group structure on the plane cubic C(M, N) by a geometric construction (the cord-and-tangent method), which depends on properties peculiar to plane cubics. Since the space curve E(M, N), the solution space of equations of the Fibonacci-Fermat type, is biregularly equivalent to C(M, N), it carries a group structure, too. It certainly is nice to recognize a group structure on the set of solutions of a system of Diophantine equations. However, we soon find that it is extremely impractical to try to copy the group structure of C(M, N) on E(M, N) via the biregular equivalence.
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© 1994 Takashi Ono
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Ono, T. (1994). Space Elliptic Curves. In: Variations on a Theme of Euler. The University Series in Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2326-7_5
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DOI: https://doi.org/10.1007/978-1-4757-2326-7_5
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