Solving the Fundamental Equation $y^{{\tau}(r)} = y$ in $\mathbb{Z}_r$

In this short note, we aim to provide a compact formula for the smallest odd integer $\tau(r) > 1$ such that the fixed-point equation $y^{\tau(r)} = y$ has the maximal set of solutions in the commutative ring of $r$-adic integers.

Short technical note isolating a fixed-point result arising from the study of constant congruence speed in radix-$r$ numeral systems, for non-prime squarefree $r > 1$.

Keywords

Numeral systems, Fixed-point equations, Number theory, p-adic integers, Commutative rings, Tetration, r-adic rings

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	0
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average

Found an issue? Give us feedback

0

Average

Green

Solving the Fundamental Equation \(y^{{\tau}(r)} = y\) in \(\mathbb{Z}_r\)

Solving the Fundamental Equation \(y^{{\tau}(r)} = y\) in \(\mathbb{Z}_r\)