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31	version[removed]Primality testing with Gaussian periods Primality testing with Gaussian periods H. W. Lenstra jr. and Carl Pomerance Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2009-02-25 13:32:39 Primality tests Finite fields Polynomials Integer factorization algorithms Field theory Prime number Root of unity Miller–Rabin primality test Elliptic curve primality testing Abstract algebra Mathematics Algebra
32	GENERATING RANDOM FACTORED GAUSSIAN INTEGERS, EASILY NOAH LEBOWITZ-LOCKARD AND CARL POMERANCE Abstract. We present a (random) polynomial-time algorithm to generate a random Gaussian integer with the uniform distribution Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2014-04-22 08:51:43 Integer factorization algorithms Modular arithmetic Primality tests Finite fields Miller–Rabin primality test Prime number Quadratic reciprocity Gaussian integer Coprime Mathematics Abstract algebra Number theory
33	A HYPERELLIPTIC SMOOTHNESS TEST, II H. W. LENSTRA Jr, J. PILA and CARL POMERANCE [Received 28 June[removed]Contents 1. Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2005-03-02 15:21:08 Algebraic curves Polynomials Analytic number theory Algebraic surfaces Elliptic curve Abelian variety Lenstra elliptic curve factorization Field Intersection number Abstract algebra Algebra Niels Henrik Abel
34	ON THE DISTRIBUTION OF SOCIABLE NUMBERS MITSUO KOBAYASHI, PAUL POLLACK, AND CARL POMERANCE Abstract. For a positive integer n, define s(n) as the sum of the proper divisors of n. If s(n) > 0, define s2 (n) = s(s(n)), and Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2008-10-07 10:39:54 Divisor function Arithmetic functions Aliquot sequence Sociable number Perfect number Prime number Normal distribution Mathematics Integer sequences Number theory
35	On pseudosquares and pseudopowers Carl Pomerance Department of Mathematics Dartmouth College Hanover, NH[removed], USA [removed] Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2008-03-17 11:52:03 Analytic number theory Conjectures Prime numbers Prime number theorem Prime-counting function Riemann hypothesis Quadratic residue Exponentiation Algebraic number field Mathematics Abstract algebra Number theory
36	Periodica Mathematica Hungarica Vol[removed]–2), (2001), pp. 191–198 THE EXPECTED NUMBER OF RANDOM ELEMENTS TO GENERATE A FINITE ABELIAN GROUP Carl Pomerance (Murray Hill) Dedicated to Professor Andr´ Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2005-03-02 15:21:08 Field theory Abelian group Niels Henrik Abel P-group Finite field Algebraic number field Index of a subgroup Solvable group Finite groups Abstract algebra Algebra Group theory
37	Amicable numbers The Memorial Conference for Felice and Paul Bateman and Heini Halberstam University of Illinois, June 5–7, 2014 Carl Pomerance, Dartmouth College Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2014-06-03 20:27:30 Integer sequences Arithmetic functions Aliquot sequence Elementary number theory Amicable numbers Divisor Orbit Pythagoras Prime number Mathematics Divisor function Number theory
38	THE ARTIN–CARMICHAEL PRIMITIVE ROOT PROBLEM ON AVERAGE SHUGUANG LI AND CARL POMERANCE Abstract. For a natural number n, let λ(n) denote the order of the largest cyclic subgroup of (Z/nZ)∗ . For a given integer a, le Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2009-10-05 14:55:48 Dirichlet character Generalized Riemann hypothesis Exponentiation Spectral theory Spectral theory of ordinary differential equations Μ operator Abstract algebra Mathematics Mathematical analysis
39	INFINITUDE OF ELLIPTIC CARMICHAEL NUMBERS AARON EKSTROM, CARL POMERANCE and DINESH S. THAKUR (September 25, 2011) Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2011-09-27 14:35:17 Integer sequences Modular arithmetic Group theory Analytic number theory Elliptic curve Primality test Coprime Prime number Carmichael number Mathematics Abstract algebra Number theory
40	version[removed]Primality testing with Gaussian periods Primality testing with Gaussian periods H. W. Lenstra jr. and Carl Pomerance Add to Reading List Source URL: www.math.dartmouth.edu Language: English - Date: 2009-12-11 15:17:22 Finite fields Primality tests Polynomials Field theory Elliptic curves Prime number Frobenius endomorphism Root of unity Miller–Rabin primality test Abstract algebra Mathematics Algebra