Mordell Conjecture

Diophantine Equations that give rise to surfaces with two or more holes have only finite manysolutions in Gaussian Integers with no common factors. Fermat's equation has Holes, so the Mordell conjecture implies that for each Integer , the Fermat Equation hasat most a finite number of solutions. This conjecture was proved by Faltings (1984).

References

Faltings, G. ``Die Vermutungen von Tate und Mordell.'' Jahresber. Deutsch. Math.-Verein 86, 1-13, 1984.

Ireland, K. and Rosen, M. ``The Mordell Conjecture.'' §20.3 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 340-342, 1990.

• Perspective
• Perspective Axis
• Perspective Center
• Perspective Collineation
• Perspective Triangles
• Perspectivity
• Pesin Theory
• Petersen Graphs
• Petersen-Shoute Theorem
• Peters Projection
• Peter-Weyl Theorem
• Petrie Polygon
• Petrov Notation
• Pfaffian Form
• p-Good Path
• p-Group
• Phase
• Phase Space
• Phase Transition
• Phasor
• Phi Curve
• Phi Number System
• Phragmén-Lindêlöf Theorem
• Phyllotaxis
• Pi