21 citations · 40 across the 14 of their papers we have counts for
14 papers
On the relation between perfect powers and tetration frozen digits
Marco Ripà
This paper provides a link between integer exponentiation and integer tetration since it is devoted to introducing some peculiar sets of perfect powers characterized by any given v…
Graham's number stable digits: An exact solution
Marco Ripà
In the decimal numeral system, we prove that the well-known Graham's number, (i.e., ( times)), and any base tetration who…
On the existence of Hamiltonian cycles in hypercubes
Gabriele Di Pietro, Marco Ripà
Building on the results of our previous work on Euclidean leaper tours, considering all integers and , we study the existence of Hamiltonian cycles in the vertex set $C(…
Euclidean Tours in Fairy Chess
Gabriele Di Pietro, Marco Ripà
The present paper aims to extend the knight's tour problem for -dimensional grids of the form to other fairy chess leapers. Accordingly, we constructively show the e…
General uncrossing covering paths inside the axis-aligned bounding box
Marco Ripà
Given the finite set of points such that ,…
Solving the years old points problem with the clockwise-algorithm
Marco Ripà
In this paper, we present the clockwise-algorithm that solves the extension in -dimensions of the infamous nine-dot problem, the well-known two-dimensional thinking outside the…
Metric spaces in chess and international chess pieces graph diameters
Marco Ripà
This paper aims to study the graph radii and diameters induced by the -dimensional versions of the well-known six international chess pieces on every finite $\{n \times n \times…
Proving the existence of Euclidean knight's tours on chessboards for
Marco Ripà
The Knight's Tour problem consists of finding a Hamiltonian path for the knight on a given set of points so that the knight can visit exactly once every vertex of the mentioned set…
Optimal cycles enclosing all the nodes of a -dimensional hypercube
Roberto Rinaldi, Marco Ripà
We solve the general problem of visiting all the nodes of a -dimensional hypercube by using a polygonal chain that has minimum link-length, and we show that this optimal v…
Number of stable digits of any integer tetration
Marco Ripà, Luca Onnis
In the present paper we provide a formula that allows to compute the number of stable digits of any integer tetration base . The number of stable digits, at the g…
Minimum-Link Covering Trails for any Hypercubic Lattice
Marco Ripà
In 1994, Kranakis et al. published a conjecture about the minimum link-length of every rectilinear covering path for the -dimensional grid $P(n,k) := \{0,1, \dots, n-1\} \times…
The congruence speed formula
Marco Ripà
We solve a few open problems related to a peculiar property of the integer tetration , which is the constancy of its congruence speed for any sufficiently large .…
Shortest polygonal chains covering each planar square grid
Marco Ripà
Given any , we constructively prove the existence of covering paths and circuits in the plane which are characterized by the same link length of the minimum-l…
On some open problems concerning perfect powers
Marco Ripà
The starting point of our paper is Kashihara's open problem number , concerning the sequence of the OEIS, asking how many terms are powers of integers. We confirm his…