801 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University of Illinois Urbana-ChampaignUS16 papers
- University of CincinnatiUS12 papers
- Northwestern UniversityUS5 papers
- University of ScrantonUS3 papers
- Adam Mickiewicz University in PoznańPL2 papers
- Baylor UniversityUS2 papers
- Carnegie Mellon UniversityUS2 papers
- Colby CollegeUS2 papers
- Eastern Illinois UniversityUS2 papers
- Ernst & Young (United States)US2 papers
- Global Social ObservatoryCH2 papers
- Gran Telescopio Canarias (Spain)ES2 papers
11 papers · 1 filter
Repeatedly Appending Any Digit to Generate Composite Numbers
Jon Grantham, Witold Jarnicki, John Rickert +1
We investigate the problem of finding integers such that appending any number of copies of the base-ten digit to yields a composite number. In particular, we prove that…
Counting fixed points and rooted closed walks of the singular map modulo powers of a prime
Joshua Holden, Pamela A. Richardson, Margaret M. Robinson
The "self-power" map modulo and its generalized form modulo are of considerable interest for both theoretical reasons and for potential…
Deconstructing the Welch Equation Using -adic Methods
Abigail Mann, Adelyn Yeoh
The Welch map is similar to the discrete exponential map , which is used in many cryptographic applications including the ElGamal signa…
Gauss Sums, Stickelberger's Theorem, and the Gras Conjecture for Ray Class Groups
Timothy All
Let be a real abelian number field and an odd prime not dividing . For a natural number , let denote the group of units of congruent to mod…
Statistics for fixed points of the self-power map
Matthew Friedrichsen, Joshua Holden
The map x -> x^x modulo p is related to a variation of the digital signature scheme in a similar way to the discrete exponentiation map, but it has received much less study. We exp…
Counting Fixed Points, Two-Cycles, and Collisions of the Discrete Exponential Function using p-adic Methods
Joshua Holden, Margaret M. Robinson
Brizolis asked for which primes p greater than 3 does there exist a pair (g, h) such that h is a fixed point of the discrete exponential map with base g, or equivalently h is a fix…
Mapping the Discrete Logarithm
Daniel R. Cloutier, Joshua Holden
The discrete logarithm is a problem that surfaces frequently in the field of cryptography as a result of using the transformation g^a mod n. This paper focuses on a prime modulus,…
Distribution of the Error in Estimated Numbers of Fixed Points of the Discrete Logarithm
Joshua Holden
Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The author and Pieter Moree, building on work…
Some Heuristics and Results for Small Cycles of the Discrete Logarithm
Joshua Holden, Pieter Moree
Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this que…
First-hit analysis of algorithms for computing quadratic irregularity
Joshua Holden
The author has previously extended the theory of regular and irregular primes to the setting of arbitrary totally real number fields. It has been conjectured that the Bernoulli num…
Comparison of algorithms to calculate quadratic irregularity of prime numbers
Joshua Holden
In previous work, the author has extended the concept of regular and irregular primes to the setting of arbitrary totally real number fields k_{0}, using the values of the zeta fun…