4 problems

Let $M$ be the map used to embed $\mathbb Z_2$ into $[0,2]$, and let $Q$ be the 3x+1 conjugacy map. Define the 3x+1 set by … A point of this set has rational coordinates when both…

Let $Q$ be the 3x+1 conjugacy map on $\mathbb Z_2$, and call a periodic orbit an odd cycle when all its elements are odd. Odd Cycles Conjecture. The function $Q$ has exactly two od…

Let $\mathbb Z^+$ denote the positive integers, let $\mathbb Z_2$ be the 2-adic integers, and let $Q$ be the 3x+1 conjugacy map. The 3x+1 problem. One should have … or equivalently…

Let $\mathbb Z_2$ denote the ring of 2-adic integers, and let $Q:\mathbb Z_2\to\mathbb Z_2$ be the 3x+1 conjugacy map. A 2-adic integer is rational when it belongs to $\mathbb Q$.…