## 127 Citations

What are the last digits of …?

- Mathematics
- 2015

We propose a class assignment where students are asked to construct and implement an efficient algorithm to calculate the last digits of a positive integral power of a positive integer. The…

The Equivalence of Giuga's and Agoh's Conjectures

- Mathematics
- 2004

In this paper we show the equivalence of the conjectures of Giuga and Agoh in a direct way which leads to a combined conjecture. This conjecture is described by a sum of fractions from which all…

Donald Arthur Preece: A life in statistics, mathematics and music

- Mathematics
- 2014

Biography and publications list for Donald Arthur Preece, who died on 6 January 2014, who made many contributions in statistics (experimental design) and in combinatorics.

Fast Digital Convolutions using Bit-Shifts

- Computer Science, MathematicsArXiv
- 2010

An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of…

On the number of primitive λ-roots

- Mathematics
- 2004

(iii) U(2) is trivial, U(4) ∼= C2, and U(2) ∼= C2 × C2a−2 for a ≥ 3. The exponent of U(n), that is, the least integer ν such that a ≡ 1 (mod n) for all integers a prime to n, is denoted by λ(n). This…

A quantum algorithm for computing the Carmichael function

- Physics, Mathematics
- 2021

Quantum computers can solve many number theory problems efficiently. Using the efficient quantum algorithm for order finding as an oracle, this paper presents an algorithm that computes the…

Korselt Rational Bases and Sets

- Mathematics
- 2019

For a positive integer $N$ and $\mathbb{A}$ a subset of $\mathbb{Q}$, let $\mathbb{A}$-$\mathcal{KS}(N)$ denote the set of $\alpha=\dfrac{\alpha_{1}}{\alpha_{2}}\in \mathbb{A}\setminus \{0,N\}$…

Number of irreducible polynomials whose compositions with monic monomials have large irreducible factors

- Mathematics
- 2019

Given a prime power $q$ and positive integers $m,t,e$ with $e > mt/2$, we determine the number of all monic irreducible polynomials $f(x)$ of degree $m$ with coefficients in $\mathbb{F}_q$ such that…

On primary Carmichael numbers

- Mathematics
- 2019

The primary Carmichael numbers were recently introduced as a special subset of the Carmichael numbers. A primary Carmichael number $m$ has the unique property that for each prime factor $p$ the sum…

Generalized Fibonacci Primitive Roots.

- Mathematics
- 2015

This note generalizes the Fibonacci primitive roots to the set of integers. An asymptotic formula for counting the number of integers with such primitive root is introduced here.