# Tagged Questions

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### How was the $3x+1$ problem checked up to $5 \times 2^{60}$?

The Wikipedia article for the Collatz conjecture states that: The conjecture has been checked by computer for all starting values up to $5 \times 2^{60} \approx 5.764 \times 10^{18}$. It gives ...
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### Collatz conjecture and related problems - mathematical machinery

Collatz conjecture stands as an open problem. That leads me to believe that the conjecture cannot be resolved by elementary means. Which brings me to my question: What techniques/machinery from ...
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### Is Collatz' conjecture the only stable solution of its type?

The Collatz Conjecture is well known with the sequence $$f(n) = \begin{cases} n/2 &;\text{if } n \equiv 0 \pmod{2}\\ k\,n+1 &; \text{if } n\equiv 1 \pmod{2} \end{cases}$$ and $k=3$; the ...
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### How can I prove that an iterated transformation describes all odd integers?

This is a question where I want to find "a best" way (or even different ways) to prove my assumption - just to widen my understanding of similar problems and how to approach them. It's a question of ...
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### Collatz-like : $(5 x \pm 1)/3$ [closed]

For a motivating start, recall the definition of the usual Collatz iteration on the integers (binding exactly one halving with each tripling), rewritten in a (slightly) unusual way. The Collatz ...
$n$,$k$, $m$, $u$ $\in$ $\Bbb N$; Let's see the following sequence: $x_0=n$; $x_m=3x_{m-1}+1$. I am afraid I am a complete noob, but I cannot (dis)prove that the following implies the ...