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Besides $3x - 1$, $5x + 1$, which variants of the $3x + 1$ problem have been proven conclusively one way or the other? [duplicate]

M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

Collatz divide by -2 instead

Collatz Conjecture, why a rate of change of $*4$ in the following?

Expression for the highest power of 2 dividing $3^a\left(2b-1\right)-1$

How to prove this inequality: $f(2h-1)≤\frac{3h-1}{2}$

Can anything be proven about this complex variant of the Collatz problem, or is it just as intractable?

Calculate the maximum in the Collatz sequence

How do I show a function on 2-adic units is continuous?

What are possibilities to disprove the Collatz Conjecture?

How far has Collatz conjecture been computationally verified?

What number has 62,118 steps ? (Collatz conjecture)

Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.

Could this odd insight help explain part of the difficulty in proving the Collatz Conjecture?

A general question about the Collatz Conjecture and finding that integer that doesn't work

Show that $2^n<2^{\lceil n \log_23\rceil}-3^n<3^n-2^n$

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Required reading on the Collatz Conjecture

Prime numbers in Collatz sequences

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Computational verification of Collatz problem

Besides $3x - 1$, $5x + 1$, which variants of the $3x + 1$ problem have been proven conclusively one way or the other? [duplicate]

M and n are positive integers such that $2^n - 3^m > 0$. Prove (or disprove) that $2^n - 3^m \geqslant 2^{n-m}-1$.

Collatz divide by -2 instead

Collatz Conjecture, why a rate of change of $*4$ in the following?

Expression for the highest power of 2 dividing $3^a\left(2b-1\right)-1$

How to prove this inequality: $f(2h-1)≤\frac{3h-1}{2}$

Can anything be proven about this complex variant of the Collatz problem, or is it just as intractable?

Calculate the maximum in the Collatz sequence

How do I show a function on 2-adic units is continuous?

What are possibilities to disprove the Collatz Conjecture?

How far has Collatz conjecture been computationally verified?

What number has 62,118 steps ? (Collatz conjecture)

Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.

Could this odd insight help explain part of the difficulty in proving the Collatz Conjecture?

A general question about the Collatz Conjecture and finding that integer that doesn't work

Show that $2^n<2^{\lceil n \log_23\rceil}-3^n<3^n-2^n$