PRIMALITY TESTING: VARIATIONS ON A THEME OF LUCAS CARL POMERANCE ´ Abstract. This survey traces an idea of Edouard Lucas that is a common element in various primality tests. These tests include those based on Fermat’s

Source URL: www.math.dartmouth.edu

• Primality tests
• AKS primality test
• Quadratic residue
• Prime number
• Lucas primality test
• Generalized Riemann hypothesis
• Mersenne prime
• Pseudoprime
• Riemann hypothesis
• Mathematics
• Abstract algebra
• Number theory

THE MAXIMAL DENSITY OF PRODUCT-FREE SETS IN Z/nZ PÄR KURLBERG, JEFFREY C. LAGARIAS, AND CARL POMERANCE A BSTRACT. This paper studies the maximal size of product-free sets in Z/nZ. These are sets of residues for which th

Source URL: www.math.dartmouth.edu

• Linear programming
• Operations research
• Vector space
• Duality
• Normal distribution
• Theorems and definitions in linear algebra
• Algebra
• Mathematics
• Convex optimization

ARE THERE COUNTER-EXAMPLES TO THE BAILLIE – PSW PRIMALITY TEST? Carl Pomerance 1984 to Arjen K. Lenstra on the defense of his doctoral thesis

Source URL: www.math.dartmouth.edu

• Numbers
• Strong pseudoprime
• Lucas pseudoprime
• Primality test
• Prime number
• Baillie–PSW primality test
• Carmichael number
• Integer factorization
• Probable prime
• Pseudoprimes
• Mathematics
• Number theory

ON BALANCED SUBGROUPS OF THE MULTIPLICATIVE GROUP CARL POMERANCE AND DOUGLAS ULMER In memory of Alf van der Poorten A BSTRACT. A subgroup H of (Z/dZ)× is called balanced if every coset of H is evenly distributed between

Source URL: www.math.dartmouth.edu

• Modular arithmetic
• Algebraic number theory
• Quadratic residue
• Finite groups
• Coprime
• Cyclic group
• Elliptic curve
• Quadratic reciprocity
• Factorial
• Mathematics
• Abstract algebra
• Number theory

([removed], 9h26) Products of ratios of consecutive integers R´egis de la Bret`eche, Carl Pomerance & G´erald Tenenbaum For Jean-Louis Nicolas, on his sixtieth birthday

Source URL: www.math.dartmouth.edu

• Sieve theory
• Exponentials
• Exponentiation
• Finite fields
• Information theory
• Jurkat–Richert theorem
• Factorization of polynomials over a finite field and irreducibility tests
• Mathematics
• Abstract algebra
• Mathematical analysis

Reduction of Huge, Sparse Matrices over Finite Fields Via Created Catastrophes Carl Pomerance and J. W. Smith CONTENTS 1. Introduction

Source URL: www.math.dartmouth.edu

SIXES AND SEVENS Carl Pomerance University of Georgia Cooper and Kennedy [1] have posed the following interesting question. For n = 0, 1, . . . ,

Source URL: www.math.dartmouth.edu

• Diophantine equations
• Integer sequences
• Mathematics
• Number theory
• Modular arithmetic

Publ. Math. Debrecen Manuscript (October 26, 2010) Primitive sets with large counting functions By Greg Martin and Carl Pomerance

Source URL: www.math.dartmouth.edu

• Combinatory logic
• Logarithm
• Mathematics
• Prime number theorem
• Exponentiation

Balanced subgroups of the multiplicative group Carl Pomerance, Dartmouth College

Source URL: www.math.dartmouth.edu

• Integer sequences
• Group theory
• Analytic number theory
• Finite fields
• Elliptic curve
• Prime number
• Factorial
• Lenstra elliptic curve factorization
• Birch and Swinnerton-Dyer conjecture
• Mathematics
• Abstract algebra
• Number theory

Some new results on λ, ϕ, and σ Carl Pomerance, Dartmouth College

Source URL: www.math.dartmouth.edu

• Mathematical analysis
• Prime numbers
• Prime-counting function
• Divisor function
• Coprime
• Spectral theory
• Normal distribution
• Spectral theory of ordinary differential equations
• Mathematics
• Number theory
• Analytic number theory