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Results tagged with collatz-conjecture
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user 8628
The Collatz Conjecture, also known as the 3n+1 conjecture, is a famous open problem named after Lothar Collatz.
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Two reasons why the Collatz conjecture could fail
Let $\mathbb{N}$ denote the set of positive integers. The Collatz function $f:\mathbb{N}\to\mathbb{N}$ is given by $f(n) = n/2$ for $n$ even and $f(n) = 3n+1$ for $n$ odd. Given $k\in\mathbb{N}$ we as …
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answer
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Generalized Collatz sequences
Let $\mathbb{N}$ denote the set of positive integers. For $k\in\mathbb{N}$ let $c_k:\mathbb{N}\to\mathbb{N}$ be defined by $x\mapsto x/2$ for $x$ even and $x\mapsto kx+1$ otherwise. The Collatz sequen …
- 48.9k
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Undecidable easy arithmetical statement
The "mortal matrix" problem: Given a set of $n\times n$-matrices with integer entries, decide whether they can be multiplied, in any order and possibly with repetition, to give the $0$-matrix. If I re …
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