Euler Quartic Conjecture
Euler 
conjectured that there are no Positive Integer solutions to the quartic DiophantineEquation
This conjecture was disproved by N. D. Elkies in 1988, who found an infinite class of solutions.See also Diophantine Equation--Quartic
References
Berndt, B. C. and Bhargava, S. ``Ramanujan--For Lowbrows.'' Amer. Math. Monthly 100, 644-656, 1993. Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 139-140, 1994. Lander, L. J.; Parkin, T. R.; and Selfridge, J. L. ``A Survey of Equal Sums of Like Powers.'' Math. Comput. 21, 446-459, 1967. Ward, M. ``Euler's Problem on Sums of Three Fourth Powers.'' Duke Math. J. 15, 827-837, 1948.
- Triangle Inscribing in an Ellipse
- Triangle of Figurate Numbers
- Triangle Postulate
- Triangle Squaring
- Triangle Tiling
- Triangle Transformation Principle
- Triangular Cupola
- Triangular Dipyramid
- Triangular Graph
- Triangular Hebesphenorotunda
- Triangular Matrix
- Triangular Number
- Triangular Orthobicupola
- Triangular Pyramid
- Triangular Square Number
- Triangular Symmetry Group
- Triangulation
- Triaugmented Dodecahedron
- Triaugmented Hexagonal Prism
- Triaugmented Triangular Prism
- Triaugmented Truncated Dodecahedron
- Triaxial Ellipsoid
- Tribar
- Tribonacci Number
- Tribox