Z-Number
A 
-number is a Real Number 
such that
for all
, 2, ..., where frac
is the fractional part of 
. Mahler (1968) showed that there is at most one-number in each interval 
for integral 
. Mahler (1968) therefore concluded that it is unlikely that any -numbers exist. The -numbers arise in the analysis of the Collatz Problem.See also Collatz Problem
References
Flatto, L. `` Guy, R. K. ``Mahler's Lagarias, J. C. ``The Mahler, K. ``An Unsolved Problem on the Powers of 3/2.'' Austral. Math. Soc. 8, 313-321, 1968. Tijdman, R. ``Note on Mahler's -Numbers and 
-Transformations.'' Symbolic Dynamics and its Applications, Contemporary Math. 135, 181-201, 1992.-Numbers.'' §E18 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 220, 1994.
Problem and its Generalizations.'' Amer. Math. Monthly 92, 3-23, 1985. http://www.cecm.sfu.ca/organics/papers/lagarias/.
-Problem.'' Kongel. Norske Vidensk Selsk. Skr. 16, 1-4, 1972.
- Aronhold Process
- Aronson's Sequence
- Arrangement
- Arrangement Number
- Array
- Arrowhead Curve
- Arrow Notation
- Arrow's Paradox
- Art Gallery Theorem
- Articulation Vertex
- Artin Braid Group
- Artinian Group
- Artinian Ring
- Artin L-Function
- Artin Reciprocity
- Artin's Conjecture
- Artin's Constant
- Artin's Reciprocity Theorem
- Artistic Series
- ASA Theorem
- Aschbacher's Component Theorem
- A-Sequence
- Associative
- Associative Algebra
- Associative Magic Square