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The Collatz conjecture is: This process will eventually reach the number 1, regardless of which positive integer is chosen initially. That is, for each n {\displaystyle n} , there is some i {\displaystyle i} with a i = 1 {\displaystyle a_{i}=1} .
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: combinatorics: Eric Dittert: 11 Eilenberg−Ganea conjecture: algebraic topology: Samuel ...
Directed graph showing the orbits of the first 1000 numbers in the Collatz conjecture. The integers from 1 to 1000 are colored from red to violet according to their ...
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
Sometimes, a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results. For example, the Riemann hypothesis is a conjecture from number theory that — amongst other things — makes predictions about the distribution of prime numbers. Few number theorists doubt that the Riemann ...
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".
But we know from Collatz conjecture § Iterating on all integers that for negative integers there are at least four different Collatz cycles. —David Eppstein 19:48, 14 August 2024 (UTC) The conjecture only pertains to positive integers, so negative numbers are not included in the analysis of the conjecture.
Goldbach's conjecture. Goldbach's weak conjecture; Second Hardy–Littlewood conjecture; Hardy–Littlewood circle method; Schinzel's hypothesis H; Bateman–Horn conjecture; Waring's problem. Brahmagupta–Fibonacci identity; Euler's four-square identity; Lagrange's four-square theorem; Taxicab number; Generalized taxicab number; Cabtaxi ...