Last updated: September 20, 2013

Current date and time:

Please send me an email about any broken links:

Factorization and Palindromic Continued Fractions (2013)

New Class number one criteria for real quadaratic fields of Richaud-Degert type and prime-producing polynomials (2013)

Exponent two in class groups of real quadratic fields...and prime-production of Euler-Rabinowitsch polynomials (2013)

Zentralblatt review of the above paper

Class Number One One Criteria for Real Quadratic Fields with Discriminant k^2p^2+-4p (2012)

Pell Equations: Non-Principal Lagrange Criteria and Central Norms (2012)

Residuacity and Genus Theory of Forms (2012)

Corrigenda for Residuacity and Genus Theory of Forms (2012)

Euler-Rabiniowitsch polynomials and class number problems revisited (2011)

A Note on Residuacity and Criteria for Prime Representation (2010)

Zentralblatt review of the above paper

Central norms: Applications to Pell's equation (2010)

Solving Diophantine equations via Lucas-Lehmer theory (2010)

Ideal class groups and generalized Euler-Rabinowitsch polynomials (2010)

A note on the negative Pell equation (2010)

Zentralblatt review of the above paper

An overview of sieve methods (2010)

A Note on the ABC Conjecture (2009)

How to Prove Fermat's Last Theorem (2009)

Characterization of D=P^2+Q^2 when gcd(P,Q)=1 and x^2-Dy^2=-1 has no integer solutions (2009)

Zentralblatt review of the above paper

Class number two for real quadratic fields of Richaud-Degert type (2009)

Zentralblatt review of the above paper

The Rabinowitsch-Mollin-Williams Theorem Revisited (2009)

Cryptography and Shift Registers (2009)

Zentralblatt review of the above paper

The Number of Bounded Solutions... (2008)

Zentralblatt review of the above paper

General Criteria for Determination of Class Groups of Real Quadratic Orders (2008)

Zentralblatt review of the above paper

Class numbers of real quadratic orders, generalized Fermat numbers, and exponential Diophantine equations (2007)

Class numbers of quadratic fields, Mersenne numbers, Fermat numbers, and exponential Diophantine equations (2007)

Zentralblatt review of the above paper

On a Generalized Kaplansky Conjecture (2007)

Diophantine Equations and Congruences (2007)

Global Versus Local Solvability of Quadratic Diophantine Equations (2006)

Quadratic Diophantine Equations x^2-Dy^2=c^2 (2006)

Zentralblatt review of the above paper

A Note on the Diophantine Equation D_1x^2+D_2=ak^n (2005)

Lagrange, Central Norms, and Quadratic Diophantine Equations (2005)

Norm Form Equations and Continued Fractions (2005)

Generalized Lagrange Criteria for Certain Quadratic Diophantine Equations (2005)

Eisenstein equations and central norms: appeared in C.R. Math. Acad. Sci. R. Can., Volume 27, (2005), 20-24;

On an elementary approach to the Lebesque-Nagell equation: appeared in Int. J. Number Theory, Volume 1, (2005), 553--561;

Necessary and Sufficient Conditions for the Central Norm to Equal 2^h in the Simple Continued Fraction Expansion of (2^h)^(1/2) for Any Odd c>1: appeared in Canad. Math. Bulletin, Volume 48, (2005), 121--132;

Class groups and quadratic diophantine equations: appeared in JP J. Algebra, Number Theory App., Volume 5, (2005), 331-347;

A Continued Fraction Approach to the Diophantine Equation ax^2-by^2=+-1 (2004): appeared in JP Jour. Alg. Number Theory and Applications, Vol. 4, pp. 159--207:

Zentralblatt review of the above paper

A Description of Continued Fraction Expansions of Quadratic Surds Represented by Polynomials (2004):

Period Lengths of Continued Fractions Involving Fibonacci Numbers (2004): appeared in The Fibonacci Quarterly volume 42, pp. 161--169

Zentralblatt review of the above paper

Infinitely Many Quadratic Diophantine Equations Solvable Everywhere Locally but Not Solvable Globally (2004): appeared in JP Journal Algebra, Number Theory and Appl., Volume 4, 353-- 362:

When the Central Norm is 2 in the Simple Continued Fraction Expansion of a Quadratic Surd: appeared in Math. Rep. Acad. Sci. Canada, Volume 26 (2004),51--54:

Zentralblatt review of the above paper

Class numbers, quadratics, and exponential Diphantine equations: appeared in JP J. Algebra Number Theory Appl., Volume 4, (2004), 537-548;

Zentralblatt review of the above paper

Construction of Families of Long Continued Fractions Revisited (2003)

Matrices and continued fractions (2003)

Infinite Families of Pellian Polynomials and Their Continued Fractions Expansions (2003)

Zentralblatt review of the above paper

Sums of Squares Revisited (2003)

On the Tate-Shafarevich Groups of y^2=x(x^2-k^2) (2003)

Zentralblatt review of the above paper

The Diophantine Equation AX^2-BY^2=C Solved Via Continued Fractions (2002)

Zentralblatt review of the above paper

Ideal Criteria for both X^2-DY^2=m_1 AND x^2-Dy^2=m_2 to have Integer Solutions for any Integers m_1, m_2 Prime to D>0 (2002)

Beepers, Creepers, and Sleepers (2002)

Continued Fraction Beepers and Fibonacci Numbers (2002)

Pellian Polynomials and Period Lengths of Continued Fractions (2002)

New Prime-Producing Quadratic Polynomials Related to Class Number One and Two (2002)

Continued Fractions and Class Number Two (2001)

Applications of a new class number two criterion for real quadratic fields (2001)

Polynomials of Pellian Type and Continued Fractions (2001)

A Simple Criterion for Solvability of both X^2-DY^2=c and x^2-Dy^2=-c (2001)

Simple Continued Fraction Solutions for Diophantine Equations (2001 )

Quadratic Diophantine Equations Determined by Continued Fractions (2001 )

Fundamental units and continued fractions two (2000)

An Upper Bound on the Least Inert Prime in a Real Quadratic Field (2000)

Cyclic Subgroups of Ideal Class Groups in Real Quadratic Orders (1999)

Palindromy and Ambiguous Ideals Revisited (1999)

Continued Fraction Gems (1999): appeared in Nieuw Arch. Wisk. Volume 17, 383--405:

All Solutions of the Diophantine Equation x^2-Dy^2=n (1998): appeared in Far East J. Math. Special Volume III, pp. 257--293:

Class Number One and Prime-Producing Quadratic Polynomials Revisited (1998 )

Jacobi Symbols, Ambiguous Ideals, and Continued Fractions (1998)

Prime Producing Quadratics (1997)

Real Prime-Producing Quadratics (1996)

Quadratic Polynomials Producing Consecutive, Distinct Primes and Class Groups of Complex Quadratic Fields (1996)

Solutions of Diophantine Equations and Divisibility of Class Numbers of Complex Quadratic Fields (1996)

The Palindromic Index... (1995)

Bounds for class numbers of quadratic orders (1995)

Quadratic Residue Covers for Certain Real Quadratic Fields (1994)

Quadratic Irrationals, Ambiguous Classes, and Symmetry in Real Quadratic Fields (1994)

Orders in Quadratic Fields I (1993)

Class Groups of Exponent Two in Real Quadratic Fields (1993)

Ambiguous Classes in Quadratic Fields (1993)

Classification and Enumeration of Real Quadratic Fields Having Exactly One Non-Inert Prime Less Than a Minkowski Bound (1993)

On the Period Length of Some Special Continued Fractions (1992)

On Real Quadratic Fields of Class Number Two (1992)

Consecutive Powers in Continued Fractions (1992)

A Complete Generalization of Yokoi's p-Invariants (1992)

Computation of the class number of a real quadratic field (1992)

Class Numbers of Real Quadratic Fields, Continued Fractions, Reduced Ideals, Prime-Producing Quadratic Polynomials and Quadratic Residue Covers (1992)

On a determination of real quadratic fields of class number one and related continued frraction period length less than 25 (1991)

Prime producing quadratic polynomials and real quadratic fields of class number one (1991)

Affirmative Solution of a Conjecture Related to a Sequence of Shanks (1991)

Solution of a Problem of Yokoi (1990)

Solution of the Class Number One Problem for Real Quadratic Fields of Extended Richaud-Degert Type (With One Possible Exception) (1990)

Applications of a new class number two criterion for real quadratic fields (1991)

Solution of a Problem of Yokoi (1990)

Continued fractions of period five and real quadratic fields of class number one(1990)

Prime Producing Quadratic Polynomials and Real Quadratic Fields of Class Number One (1989)

Class Number One for Real Quadratic Fields, Continued Fractions, and Reduced Ideals (1989)

Period Four and Real Quadratic Fields of Class Number One (1989)

Invariants in Group Rings (1988)

Proper Differences of Non-Square Powerful Numbers (1988)

A Conjecture of S. Chowla Via the Generalized Riemann Hypothesis (1988)

Necessary and Sufficient Conditions for the Class Number of a Real Quadratic Field to be One, and a Conjecture of S. Chowla (1988)

Generalized Fibonacci Primitive Roots, and Class Numbers of Real Quadratic Fields (1988)

On Prime Valued Polynomials and Class Numbers of Real Quadratic Fields (1988)

Class Number One Criteria for Real Quadratic Fields I (1987)

Class Number One Criteria for Real Quadratic Fields II (1987)

AMS review of the above two papers

The Power of Powerful Numbers (1987)

On Permutation Polynomials Over Finite Fields (1987)

Class Numbers of Quadratic Fields Determined by Solvability of Diophantine Equations (1987)

Class Groups, Totally Positive Units, and Squares (1986)

On Class Numbers of Quadratic Extensions of Algebraic Number Fields (1986)

Diophantine Equations and Class Numbers (1986)

More on the Schur Group of a Commutative Ring (1985)

The Schur Group of a Commutative Ring (1985)

Uniform Distribution of Hasse Invariants (1985)

Admissible Groups, Symmetric Factor Sets, and Simple Algebras (1984)

Minimal Cyclotomic Splitting Fields for Group Characters (1984)

Class Numbers and a Generalized Fermat Theorem (1983)

Totally Positive Units and Squares (1983)

Cyclotomic Splitting Fields (1982)

Cyclotomic Division Algebra (1981)

Induced p-elements in the Schur Group (1980)

Splitting Fields and Group Characters (Crelle's Journal 1980)

Uniform Distribution Classified (1979)

Algebras With Uniformly Distributed Invariants (1977)

Genaralized Uniform Distribution of Hasse Invariants (1977)

Uniform Distribution and the Schur Group (1976)

Uniform Distribution and Real Fields (1976)