All Questions

The conjecture is as follows: Let $n\in\mathbb{N}\setminus\{1\}$. Define $a(n)=2^n+1$ and the set: $$S(n) = \{ (a(n)^m+1)/2\ :\ m\in \mathbb{N}_0\}.$$ Then for all $c\in\mathbb{N}$, the number $(a(n)...

The conjecture says that for any a, b belong to the the set of non-negative integers ($a$ and $b$ are not necessarily distinct), taking any natural value of $c$; we have always that $$(10^c-1) \cdot \...

This is sort of a companion to my question Number of trivializations of a trivial word in the free group (which in turn is motivated by my earlier question here). It turns out that that question may ...