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The Collatz conjecture [a] is one of the most famous unsolved problems in mathematics. ... The standard Collatz function is given by P = 2, ...
Chowla conjecture: Möbius function: ⇒Sarnak conjecture [6] [7] Sarvadaman Chowla: Collatz conjecture: number theory: Lothar Collatz: 1440 Cramér's conjecture: number theory: Harald Cramér: 32 Conway's thrackle conjecture: graph theory: John Horton Conway: 150 Deligne conjecture: monodromy: Pierre Deligne: 788 Dittert conjecture ...
A refresher on the Collatz Conjecture: It’s all about that function f(n), shown above, which takes even numbers and cuts them in half, while odd numbers get tripled and then added to 1. Take any ...
Collatz conjecture (also known as the + conjecture) Eden's conjecture that the supremum of the local Lyapunov dimensions on the global attractor is achieved on a stationary point or an unstable periodic orbit embedded into the attractor.
Examples of non-normalizing systems (not weakly or strongly) include counting to infinity (1 ⇒ 2 ⇒ 3 ⇒ ...) and loops such as the transformation function of the Collatz conjecture (1 ⇒ 2 ⇒ 4 ⇒ 1 ⇒ ..., it is an open problem if there are any other loops of the Collatz transformation). [7]
The conjecture is that there is a simple way to tell whether such equations have a finite or infinite number of rational solutions. More specifically, the Millennium Prize version of the conjecture is that, if the elliptic curve E has rank r , then the L -function L ( E , s ) associated with it vanishes to order r at s = 1 .
It is Gardner's 10th collection of columns, and includes material on Conway's Game of Life, supertasks, intransitive dice, braided polyhedra, combinatorial game theory, the Collatz conjecture, mathematical card tricks, and Diophantine equations such as Fermat's Last Theorem. [3]
In algebra, the 3x + 1 semigroup is a special subsemigroup of the multiplicative semigroup of all positive rational numbers. [1] The elements of a generating set of this semigroup are related to the sequence of numbers involved in the still open Collatz conjecture or the "3x + 1 problem".