Lenny Jones

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All published works

Action	Title	Year	Authors
+ PDF Chat	Monogenic Even Cyclic Sextic Polynomials	2025	Lenny Jones
+ PDF Chat	Monogenic cyclic cubic trinomials	2025	Lenny Jones
+ PDF Chat	Monogenic cyclic trinomials of the form $x^4+cx+d$	2025	Lenny Jones
+ PDF Chat	Monogenic $S_3$-cubic polynomials and class numbers of associated quadratic fields	2024	Lenny Jones
+ PDF Chat	Monogenic Cyclic Cubic Trinomials	2024	Lenny Jones
+ PDF Chat	Monogenic cyclic trinomials of the form $x^4+cx+d$	2024	Lenny Jones
+ PDF Chat	Monogenic Trinomials of the form x4 + ax3 + d and their Galois groups	2024	Joshua Harrington Lenny Jones
+ PDF Chat	The monogenicity and Galois groups of certain reciprocal quintinomials	2024	Lenny Jones
+ PDF Chat	MONOGENIC QUARTIC POLYNOMIALS AND THEIR GALOIS GROUPS	2024	Joshua Harrington Lenny Jones
+	MONOGENIC EVEN QUARTIC TRINOMIALS	2024	Lenny Jones
+ PDF Chat	Monogenic trinomials of the form $x^4+ax^3+d$ and their Galois groups	2024	Joshua Harrington Lenny Jones
+ PDF Chat	Monogenic Cyclic Quartic Trinomials	2024	Lenny Jones
+ PDF Chat	Monogenic Even Octic Polynomials and Their Galois Groups	2024	Lenny Jones
+ PDF Chat	Monogenic Quartic Polynomials and Their Galois Groups	2024	Joshua Harrington Lenny Jones
+ PDF Chat	Reciprocal Monogenic Septinomials of Degree 2<sup>n</sup>3	2024	Lenny Jones
+ PDF Chat	A New Condition for $k$-Wall–Sun–Sun Primes	2024	Lenny Jones
+ PDF Chat	THE MONOGENICITY OF POWER-COMPOSITIONAL CHARACTERISTIC POLYNOMIALS	2024	Lenny Jones
+	Reducibility type of polynomials modulo a prime	2023	Joshua Harrington Lenny Jones
+ PDF Chat	GENERALIZED WALL-SUN-SUN PRIMES AND MONOGENIC POWER-COMPOSITIONAL TRINOMIALS	2023	Lenny Jones
+ PDF Chat	On the monogenicity of power-compositional Shanks polynomials	2023	Lenny Jones
+	A NOTE ON GENERALISED WALL–SUN–SUN PRIMES	2023	Joshua Harrington Lenny Jones
+	Generalized Wall-Sun-Sun primes and monogenic power compositional trinomials	2023	Lenny Jones
+	A new condition for $k$-Wall-Sun-Sun primes	2023	Lenny Jones
+	On the monogenicity of power-compositional Shanks polynomials	2023	Lenny Jones
+	The Monogenicity of Power-Compositional Characteristic Polynomials	2023	Lenny Jones
+	On necessary and sufficient conditions for the monogeneity of a certain class of polynomials	2022	Lenny Jones
+	RECIPROCAL MONOGENIC QUINTINOMIALS OF DEGREE	2022	Lenny Jones
+	Infinite families of monogenic quadrinomials, quintinomials and sextinomials	2022	Lenny Jones
+	The Irreducibility and Monogenicity of Power-Compositional Trinomials	2022	Joshua Harrington Lenny Jones
+ PDF Chat	The monogenity of power-compositional Eisenstein polynomials	2022	Lenny Jones
+	A Connection Between the Monogenicity of Certain Power-Compositional Trinomials and $k$-Wall-Sun-Sun Primes	2022	Lenny Jones
+	MONOGENICALLY STABLE POLYNOMIALS	2021	Lenny Jones
+	When Does F(α<sup><i>d</i></sup>) = F(α)?	2021	Lenny Jones
+ PDF Chat	Monogenic Pisot and Anti-Pisot Polynomials	2021	Lenny Jones
+	Some new polynomial discriminant formulas	2021	Joshua Harrington Lenny Jones
+ PDF Chat	Monogenic trinomials with non-squarefree discriminant	2021	Lenny Jones Daniel White
+	Characteristic polynomials of simple non-ordinary abelian varieties	2021	Lenny Jones
+	Infinite families of non-monogenic trinomials	2021	Lenny Jones
+ PDF Chat	Monogenic Cyclotomic compositions	2021	Joshua Harrington Lenny Jones
+ PDF Chat	CHARACTERISTIC POLYNOMIALS OF SIMPLE ORDINARY ABELIAN VARIETIES OVER FINITE FIELDS	2021	Lenny Jones
+	Characteristic Polynomials of Simple Ordinary Abelian Varieties over Finite Fields.	2020	Lenny Jones
+	Some new infinite families of monogenic polynomials with non-squarefree discriminant	2020	Lenny Jones
+	Monogenic reciprocal trinomials and their Galois groups	2020	Lenny Jones
+	Sextic reciprocal monogenic dihedral polynomials	2020	Lenny Jones
+ PDF Chat	Monogenic Binomial Compositions	2020	Joshua Harrington Lenny Jones
+	Generating Infinite Families of Monogenic Polynomials Using a New Discriminant Formula	2020	Lenny Jones
+	Characteristic Polynomials of Simple Ordinary Abelian Varieties over Finite Fields	2020	Lenny Jones
+ PDF Chat	Monogenic polynomials with non-squarefree discriminant	2019	Lenny Jones
+	Monogenic cyclotomic compositions	2019	Joshua Harrington Lenny Jones
+	Monogenic trinomials with non-squarefree discriminant	2019	Lenny Jones Daniel White
+	A BRIEF NOTE ON SOME INFINITE FAMILIES OF MONOGENIC POLYNOMIALS	2019	Lenny Jones
+	Monogenic cyclotomic compositions	2019	Joshua Harrington Lenny Jones
+	Monogenic trinomials with non-squarefree discriminant	2019	Lenny Jones Daniel White
+	A modification of a problem of Diophantus	2018	Joshua Harrington Lenny Jones
+	A new condition equivalent to the Ankeny–Artin–Chowla conjecture	2018	Joshua Harrington Lenny Jones
+	Infinite families of monogenic trinomials and their Galois groups	2018	Lenny Jones Tristan Phillips
+	An Equation Involving Arithmetic Functions and Riesel Numbers.	2018	Joshua Harrington Lenny Jones
+	AN INFINITE FAMILY OF NINTH DEGREE DIHEDRAL POLYNOMIALS	2017	Lenny Jones Tristan Phillips
+	Differences between elements of the same order in a finite field	2017	Joshua Harrington Lenny Jones
+	The irreducibility of power compositional sextic polynomials and their Galois groups	2017	Joshua Harrington Lenny Jones
+	Primes in Shifted Sums of Lucas Sequences.	2017	Lenny Jones Lawrence Somer
+	Arithmetic Progressions of Polygonal Numbers With Common Difference a Polygonal Number.	2017	Lenny Jones Tristan Phillips
+	Primefree shifted Lucas sequences of the second kind	2016	Dan Ismailescu Lenny Jones Tristan Phillips
+	New primitive covering numbers and their properties	2016	Joshua Harrington Lenny Jones Tristan Phillips
+ PDF Chat	The irreducibility of polynomials related to a question of Schur	2016	Lenny Jones Alicia Lamarche
+ PDF Chat	On primitive covering numbers	2016	Lenny Jones Daniel White
+	A Group-theoretic Approach to Covering Systems	2016	Lenny Jones Daniel White
+	A Problem Related to a Conjecture of Polignac.	2016	Kellie Bresz Lenny Jones Alicia Lamarche Maria Markovich
+	On the Congruence xx ≡ x (mod n).	2016	James Hammer Joshua Harrington Lenny Jones
+	A problem of Diophantus modulo a prime	2016	Joshua Harrington Lenny Jones
+	Perfect power Riesel numbers	2015	Carrie E. Finch Lenny Jones
+	Primefree shifted Lucas sequences	2015	Lenny Jones
+	Extending a Theorem of Pillai to Quadratic Sequences.	2015	Joshua Harrington Lenny Jones
+	Generating d-Composite Sandwich Numbers.	2015	Lenny Jones Alicia Lamarche
+ PDF Chat	Generalizing a theorem of Schur	2014	Lenny Jones
+ PDF Chat	Characterizing Finite Groups Using the Sum of the Orders of the Elements	2014	Joshua Harrington Lenny Jones Alicia Lamarche
+	On Primitive Covering Numbers	2014	Lenny Jones Daniel White
+	Generating Composite Sequences by Appending Digits to Special Types of Integers	2014	Lenny Jones Maria Markovich
+ PDF Chat	Infinite Families of A<sub>4</sub>-Sextic Polynomials	2014	Joshua Ide Lenny Jones
+	Representing Integers as the Sum of Two Squares in the Ring $\Z_n$	2014	Joshua Harrington Lenny Jones Alicia Lamarche
+	Representing Integers as the Sum of Two Squares in the Ring Z n	2014	Joshua Harrington Lenny Jones Alicia Lamarche
+	On Primitive Covering Numbers	2014	Lenny Jones Daniel White
+	THE REDUCIBILITY OF CONSTANT-PERTURBED PRODUCTS OF CYCLOTOMIC POLYNOMIALS	2013	Joshua Harrington Lenny Jones Daniel White
+ PDF Chat	A class of irreducible polynomials	2013	Joshua Harrington Lenny Jones
+ PDF Chat	Maximal denumerant of a numerical semigroup with embedding dimension less than four	2012	Lance Bryant James Hamblin Lenny Jones
+	Nonlinear Sierpiński and Riesel numbers	2012	Carrie E. Finch Joshua Harrington Lenny Jones
+	Enumerating invariant subspaces of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>	2012	Josh Ide Lenny Jones
+	Corrigendum to “Polynomial Cunningham chains” [J. Number Theory 131 (11) (2011) 2100–2106]	2012	Lenny Jones
+ PDF Chat	Sierpiński Numbers in Imaginary Quadratic Fields	2012	Lenny Jones Daniel White
+ PDF Chat	Multiplicative bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group	2012	Andrew Francis Lenny Jones
+	Enumerating Invariant Subspaces of ${\mathbb R}^n$	2012	Josh Ide Lenny Jones
+	Fibonacci Variations of a Conjecture of Polignac	2012	Lenny Jones
+	A Variation on the Money-Changing Problem	2012	Lance Bryant James Hamblin Lenny Jones
+ PDF Chat	Using Lucas sequences to generalize a theorem of Sierpiński	2012	Lenny Jones
+	Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group	2012	Andrew Francis Lenny Jones
+ PDF Chat	On three questions concerning groups with perfect order subsets	2011	Lenny Jones Kelly Toppin
+ PDF Chat	Polynomial Cunningham chains	2011	Lenny Jones
+	Using Lucas Sequences to Generalize a Theorem of Sierpi\'nski	2011	Lenny Jones
+	Polynomial Cunningham Chains	2011	Lenny Jones
+	When Does Appending the Same Digit Repeatedly on the Right of a Positive Integer Generate a Sequence of Composite Integers?	2011	Lenny Jones
+	Appending Digits to Generate an Infinite Sequence of Composite Numbers	2011	Lenny Jones Daniel White
+	Using Lucas Sequences to Generalize a Theorem of Sierpiński	2011	Lenny Jones
+	Polynomial Cunningham Chains	2011	Lenny Jones
+	On the Iteration of a Function Related to Euler's φ-Function	2010	Joshua Harrington Lenny Jones
+	POLYNOMIAL VARIATIONS ON A THEME OF SIERPIŃSKI	2009	Lenny Jones
+	A new integral basis for the centre of the Iwahori–Hecke algebra of type A	2008	Andrew Francis Lenny Jones
+	An Equality for Parts in Partitions of n: 11237.	2008	Lenny Jones Rachel Keller Toni Ernvall Anne-Maria Ernvall-Hytönen
+	Primes with Special Primitive Roots: 11254.	2008	Lenny Jones Toni Ernvall
+	On the square root of the centre of the Hecke algebra of type A	2007	Andrew Francis Lenny Jones
+ PDF Chat	On the square root of the centre of the Hecke algebra of type <i>A</i>	2007	Andrew Francis Lenny Jones
+	Variations on a Theme of Sierpinski	2007	Lenny Jones
+	Monomial bases for the centres of the group algebra and Iwahori--Hecke algebra of S_4	2007	Andrew Francis Lenny Jones
+	A new integral basis for the centre of the Hecke algebra of type A	2007	Andrew Francis Lenny Jones
+	On the square root of the centre of the Hecke algebra of type A	2007	Andrew Francis Lenny Jones
+	Sequences of Reducible f0; 1g{Polynomials Modulo a Prime	2006	Judith Canner Lenny Jones Joseph Purdom
+ PDF Chat	On the Irreducibility of {-1,0,1}-Quadrinomials	2006	Carrie E. Finch Lenny Jones
+	ON THE IRREDUCIBILITY OF {! 1,0,1}-QUADRINOMIALS	2006	Carrie E. Finch Lenny Jones
+	On bases of centres of Iwahori–Hecke algebras of the symmetric group	2005	Andrew Francis Lenny Jones
+ PDF Chat	An extension of a theorem of D. H. Lehmer	2004	Lenny Jones
+	On bases of centres of Iwahori-Hecke algebras of the symmetric group	2004	Andrew Francis Lenny Jones
+	Euler to the Rescue: 10869	2003	Lenny Jones Florian Luca
+	Homogeneously generated groups	2003	Richard Foote Lenny Jones
+	A Curious Connection Between Fermat Numbers and Finite Groups	2002	Carrie E. Finch Lenny Jones
+	Finite Groups That Have Exactly <i>n</i> Elements of Order <i>n</i>	2002	Carrie E. Finch Richard Foote Lenny Jones Donald Spickler
+	Finite Groups That Have Exactly n Elements of Order n	2002	Carrie E. Finch Richard Foote Lenny Jones Donald Spickler
+	A Curious Connection between Fermat Numbers and Finite Groups	2002	Carrie E. Finch Lenny Jones
+	A Polynomial Approach to a Diophantine Problem	1999	Lenny Jones
+	A Divisibility Property of Primes: 10544	1998	Lenny Jones Kevin Ford Charles Lanski
+ PDF Chat	Centers of generic Hecke algebras	1990	Lenny Jones
+ PDF Chat	Centers of Generic Hecke Algebras	1990	Lenny Jones
+	Sequences, Series, and Pascal's Triangle	1983	Lenny Jones

Common Coauthors

Coauthor	Papers Together
Joshua Harrington	23
Andrew Francis	10
Daniel White	10
Carrie E. Finch	8
Alicia Lamarche	6
Joshua Harrington	5
Tristan Phillips	5
Richard Foote	3
Maria Markovich	2
Toni Ernvall	2
James Hamblin	2
Josh Ide	2
Donald Spickler	2
Lance Bryant	2
Charles Lanski	1
James Hammer	1
Joseph Purdom	1
Kevin Ford	1
Judith Canner	1
Lawrence Somer	1
Kelly Toppin	1
Anne-Maria Ernvall-Hytönen	1
Florian Luca	1
Kellie Bresz	1
Dan Ismailescu	1
Joshua Ide	1
Rachel Keller	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	A Course in Computational Algebraic Number Theory	1993	Henri Cohen	14
+	Polynomials with Special Regard to Reducibility	2000	Andrzej Schinzel	13
+	The ABC conjecture, arithmetic progressions of primes and squarefree values of polynomials at prime arguments	2014	Héctor Pastén	13
+ PDF Chat	Squarefree values of trinomial discriminants	2015	David W. Boyd Greg Martin Mark Thom	11
+	Characterization of primes dividing the index of a trinomial	2017	Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan	10
+ PDF Chat	Square-free values of f(p), f cubic	2014	H. A. Helfgott	10
+	On certain pure sextic fields related to a problem of Hasse	2016	Shahzad Ahmad Toru Nakahara Abdul Hameed	10
+	Power integral bases for certain pure sextic fields	2014	Shahzad Ahmad Toru Nakahara Syed Muhammad Husnine	10
+ PDF Chat	A construction of polynomials with squarefree discriminants	2012	Kiran S. Kedlaya	9
+	The Factorization of the Cyclotomic Polynomials mod p	1968	W. J. Guerrier	8
+	On integers of the forms kr−2n and kr2n+1	2003	Yong-Gao Chen	8
+	Integral bases and monogenity of pure fields	2016	István Gaál László Remete	8
+	$A_4$-Sextic Fields with a Power Basis	2007	Daniël Eloff Blair K. Spearman Kenneth S. Williams	8
+	Algebraic Number Theory	1999	Jürgen Neukirch	8
+	Infinite families of monogenic trinomials and their Galois groups	2018	Lenny Jones Tristan Phillips	8
+ PDF Chat	Discriminants of Chebyshev radical extensions	2014	T. Alden Gassert	8
+	On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture	2008	Michael Filaseta Carrie E. Finch Mark Kozek	7
+	A Classical Introduction to Modern Number Theory	1982	Kenneth Ireland Michael Rosen	7
+	On power basis of a class of algebraic number fields	2016	Bablesh Jhorar Sudesh K. Khanduja	7
+ PDF Chat	Monogenic polynomials with non-squarefree discriminant	2019	Lenny Jones	6
+ PDF Chat	On an irreducibility theorem of A. Schinzel associated with coverings of the integers	2000	Michael Filaseta Kevin Ford Sergeĭ Konyagin	6
+	Fibonacci Series Modulo <i>m</i>	1960	D. D. Wall	6
+	The Minimal Basis for the Centre of an Iwahori–Hecke Algebra	1999	Andrew Francis	6
+ PDF Chat	Monogenic A_4 quartic fields	2006	Blair K. Spearman	6
+ PDF Chat	Monogenic Cyclotomic compositions	2021	Joshua Harrington Lenny Jones	5
+	Blocks and Idempotents of Hecke Algebras of General Linear Groups	1987	Richard Dipper Gordon James	5
+ PDF Chat	A Classical Introduction to Modern Number Theory	1990	Kenneth Ireland Michael Rosen	5
+ PDF Chat	Monogenic Binomial Compositions	2020	Joshua Harrington Lenny Jones	5
+	Some new infinite families of monogenic polynomials with non-squarefree discriminant	2020	Lenny Jones	5
+	Generating Infinite Families of Monogenic Polynomials Using a New Discriminant Formula	2020	Lenny Jones	5
+	On the Numerical Factors of the Arithmetic Forms α n ± β n	1913	R. D. Carmichael	5
+	Centers and Simple Modules for Iwahori-Hecke Algebras	1997	Meinolf Geck Raphaël Rouquier	5
+	Centres of Hecke algebras: The Dipper–James conjecture	2006	Andrew Francis J. J. Graham	5
+	Fibonacci Variations of a Conjecture of Polignac	2012	Lenny Jones	5
+ PDF Chat	Zur Arithmetik der Polynome	1922	Trygve Nagel	4
+ PDF Chat	The simplest cubic fields	1974	Daniel Shanks	4
+	Elementary Methods in Number Theory	2000	Melvyn B. Nathanson	4
+	Diophantine Equations and Power Integral Bases	2019	István Gaál	4
+	A BRIEF NOTE ON SOME INFINITE FAMILIES OF MONOGENIC POLYNOMIALS	2019	Lenny Jones	4
+	On prime divisors of the index of an algebraic integer	2016	Anuj Jakhar Sudesh K. Khanduja Neeraj Sangwan	4
+	The idempotents of the symmetric group and Nakayama's conjecture	1983	G.E Murphy	4
+ PDF Chat	Centers of generic Hecke algebras	1990	Lenny Jones	4
+	When Does Appending the Same Digit Repeatedly on the Right of a Positive Integer Generate a Sequence of Composite Integers?	2011	Lenny Jones	4
+	Number Theory for the Millennium I	2002	Michael A. Bennett	4
+	A covering system whose smallest modulus is 40	2008	Pace P. Nielsen	4
+	On the Existence of Absolutely Simple Abelian Varieties of a Given Dimension over an Arbitrary Field	2002	Everett W. Howe Hui June Zhu	4
+	Nonlinear Sierpiński and Riesel numbers	2012	Carrie E. Finch Joshua Harrington Lenny Jones	4
+	Applications of sieve methods to the theory of numbers	1976	C. Hooley	4
+	On integers of the form 𝑘2ⁿ+1	2000	Yong-Gao Chen	4
+ PDF Chat	Abelian varieties over finite fields	1969	William C. Waterhouse	3