Diophantus Property
A set of Positive Integers 
satisfies the Diophantus property 
of order 
if, for all
, ..., 
with 
,
 | (1) |
and 
are Integers. The set 
is called a Diophantine -tuple. Fermat found thefirst 
quadruple: 
. General quadruples are | (2) |
are Fibonacci Numbers, and | (3) |
The quadruplet
 | (4) |
(Dujella 1996). Dujella (1993) showed there exist no Diophantine quadruples 
.
References
Aleksandriiskii, D. Arifmetika i kniga o mnogougol'nyh chislakh. Moscow: Nauka, 1974. Brown, E. ``Sets in Which Davenport, H. and Baker, A. ``The Equations Dujella, A. ``Generalization of a Problem of Diophantus.'' Acta Arithm. 65, 15-27, 1993. Dujella, A. ``Diophantine Quadruples for Squares of Fibonacci and Lucas Numbers.'' Portugaliae Math. 52, 305-318, 1995. Dujella, A. ``Generalized Fibonacci Numbers and the Problem of Diophantus.'' Fib. Quart. 34, 164-175, 1996. Hoggatt, V. E. Jr. and Bergum, G. E. ``A Problem of Fermat and the Fibonacci Sequence.'' Fib. Quart. 15, 323-330, 1977. Jones, B. W. ``A Variation of a Problem of Davenport and Diophantus.'' Quart. J. Math. (Oxford) Ser. (2) 27, 349-353, 1976.
is Always a Square.'' Math. Comput. 45, 613-620, 1985.
and 
.'' Quart. J. Math. (Oxford) Ser. 2 20, 129-137, 1969.
- Fiber
- Fiber Bundle
- Fiber Space
- Fibonacci Dual Theorem
- Fibonacci Hyperbolic Cosine
- Fibonacci Hyperbolic Cotangent
- Fibonacci Hyperbolic Sine
- Fibonacci Hyperbolic Tangent
- Fibonacci Identity
- Fibonacci Matrix
- Fibonacci n-Step Number
- Fibonacci Number
- Fibonacci Polynomial
- Fibonacci Pseudoprime
- Fibonacci Q-Matrix
- Fibonacci Sequence
- Fibration
- Field
- Field Axioms
- Field Extension
- Fields Medal
- Fifteen Theorem
- Figurate Number
- Figurate Number Triangle
- Figure Eight Knot