# Tagged Questions

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### Modified Collatz Problem

How can one prove for all $n \in \mathbb N$ that the following sequence always results in $1$: Choose $m$ $x_1 = m$ x_{n+1} = \begin{cases} x_n/2 & \text{if $x_n$ is even} \\ \\ x_n + 1 & ...
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### My problem in understanding the minimal counterexample technique

If minimal counterexample method of proof is to assume to opposite of an argument is true and then finding a counterexample for the opposite and then concluding the validity of the original argument, ...
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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 ...
$n$,$k$, $m$, $u$ $\in$ $\Bbb N$; 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 ...