Lawrence Somer

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All published works

Action	Title	Year	Authors
+ PDF Chat	Second-order linear recurrences with identically distributed residues modulo p^e	2024	Lawrence Somer Michal Křı́žek
+ PDF Chat	Regular Tessellations of Maximally Symmetric Hyperbolic Manifolds	2024	Jan Brandts Michal Křı́žek Lawrence Somer
+	On Tetrahedral and Square Pyramidal Numbers	2023	Lawrence Somer Michal Křı́žek
+	Frobenius, Lucas, and Dickson Pseudoprimes	2022	Lawrence Somer Michal Křı́žek
+	Second-Order Linear Recurrences Having Arbitrarily Large Defect Modulo <i>p</i>	2021	Lawrence Somer Michal Křı́žek
+	Fibonacci and Lucas Numbers	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Special Types of Primes	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	From Great Discoveries in Number Theory to Applications	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Prime and Composite Numbers	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Further Applications of Number Theory	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Properties of Prime Numbers	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Further Special Types of Integers	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	On a Connection of Number Theory with Graph Theory	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Pseudoprimes	2021	Michal Křı́žek Lawrence Somer Alena Šolcová
+	Nondefective Integers With Respect to Certain Lucas Sequences of the Second Kind.	2018	Lawrence Somer Michal Křı́žek
+	Primes in Shifted Sums of Lucas Sequences.	2017	Lenny Jones Lawrence Somer
+	On Primes in Lucas Sequences	2015	Lawrence Somer Michal Křížek
+	On the symmetric digraphs from the <i>k</i>th power mapping on finite commutative rings	2014	Guixin Deng Lawrence Somer
+	Easy Criteria to Determine if a Prime Divides Certain Second-Order Recurrences	2013	Lawrence Somer Michal Křı́žek
+	Power Digraphs Modulo <i>n</i> are Symmetric of order <i>M</i> if and only if <i>M</i> is Square Free	2012	Lawrence Somer Michal Křı́žek
+ PDF Chat	The structure of digraphs associated with the congruence x k ≡ y (mod n)	2011	Lawrence Somer Michal Křı́žek
+	On the Complexity of Testing Elite Primes	2011	Michal Křı́žek Florian Luca Igor E. Shparlinski Lawrence Somer
+	Lucas ( <i>a</i> <sub>1</sub> , <i>a</i> <sub>2</sub> , …, <i> a <sub>k</sub> </i> = ±1) Pseudoprimes	2010	Lawrence Somer Curtis Cooper
+ PDF Chat	Stability Classes of Second-Order Linear Recurrences Modulo $2^k$ II	2010	Walter Carlip Lawrence Somer
+	Lucas Pseudoprimes of Special Types	2008	Lawrence Somer
+	On symmetric digraphs of the congruence <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mo>≡</mml:mo><mml:mi>y</mml:mi><mml:mspace width="0.16667em" /><mml:mrow><mml:mo>(</mml:mo><mml:mo>mod</mml:mo><mml:mspace width="0.334em" /><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>	2008	Lawrence Somer Michal Křı́žek
+ PDF Chat	Square-free Lucas d-pseudoprimes and Carmichael-Lucas numbers	2007	Walter Carlip Lawrence Somer
+ PDF Chat	Primitive Lucas d-pseudoprimes and Carmichael–Lucas numbers	2007	Walter Carlip Lawrence Somer
+	On semiregular digraphs of the congruence $x^k\equiv y \hspace{4.44443pt}(\@mod \; n)$	2007	Lawrence Somer Michal Křı́žek
+	Lucas Sequences for which 4 \| ø (\|u <sub>n</sub> \|) for almost all <i>n</i>	2006	Florian Luca Lawrence Somer
+	Structure of digraphs associated with quadratic congruences with composite moduli	2006	Lawrence Somer Michal Křı́žek
+	Lucas Sequences { <i> U <sub>Κ</sub> </i> } for which <i>U</i> <sub> 2 <i>p</i> </sub> and <i> U <sub>p</sub> </i> are Pseudoprimes for Almost all Primes <i>p</i>	2006	Lawrence Somer
+ PDF Chat	On a Connection of Number Theory with Graph Theory	2004	Lawrence Somer Michal Křı́žek
+	A Further Note on Lucasian Numbers	2004	Lawrence Somer
+	The Existence of Special Multipliers of Second-Order Recurrence Sequences	2003	Walter Carlip Lawrence Somer
+	LUCAS SEQUENCES {Uk} FOR WHICH U2p AND Up ARE PSEUDOPRIMES FOR ALMOST ALL PRIMES p	2003	Lawrence Somer
+	17 necessary and sufficient conditions for the primality of Fermat numbers	2003	Michal Křı́žek Lawrence Somer
+	On the Convergence of Series of Reciprocals of Primes Related to the Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Connections of Fermat Numbers with Pascal’s Triangle	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	The Irrationality of the Sum of Some Reciprocals	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Generalizations of Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	The Most Beautiful Theorems on Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Fermat Primes and a Diophantine Equation	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Fermat Number Transform and Other Applications	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Basic Properties of Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Euclidean Construction of the Regular Heptadecagon	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Primality of Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Fermat’s Little Theorem, Pseudoprimes, and Superpseudoprimes	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	The Proof of Gauss’s Theorem	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Factors of Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	Divisibility of Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer
+	17 lectures on Fermat numbers : from number theory to geometry	2001	Michal Křı́žek Florian Luca Lawrence Somer Alena Šolcová
+ PDF Chat	A necessary and sufficient condition for the primality of Fermat numbers	2001	Michal Křı́žek Lawrence Somer
+	17 Lectures on Fermat Numbers	2001	Michal Křı́žek Florian Luca Lawrence Somer
+	Special Multipliers of Lucas Sequences Modulo pr	1999	Lawrence Somer
+	Pseudoprimes, Perfect Numbers, and a Problem of Lehmer	1998	Walter Carlip Eliot Jacobson Lawrence Somer
+	On Lucas d-Pseudoprimes	1998	Lawrence Somer
+	A Criterion For Stability of Two-Term Recurrence Sequences Modulo Odd Primes	1998	Walter Carlip Eliot Jacobson Lawrence Somer
+	On Lucasian Numbers	1997	Peter Hilton Jean Pedersen Lawrence Somer
+	Periodicity properties of <i>k</i>th order linear recurrences whose characteristic polynomial splits completely over a finite field, II	1996	Lawrence Somer
+	Distribution of Residues of Certain Second-Order Linear Recurrences Modulo p-III	1996	Lawrence Somer
+	Divisibility of Terms in Lucas Sequences of the Second Kind by Their Subscripts	1996	Lawrence Somer
+	Periodicity properties of 𝑘th order linear recurrences whose characteristic polynomial splits completely over a finite field. I	1994	Lawrence Somer
+	Upper Bounds for Frequencies of Elements in Second-Order Recurrences over A Finite Field	1993	Lawrence Somer
+	Possible Restricted Periods of Certain Lucas Sequences Modulo P	1991	Lawrence Somer
+	On Even Fibonacci Pseudoprimes	1991	Lawrence Somer
+	Period Patterns of Certain Second-Order Linear Recurrences Modulo a Prime	1991	David Banks Lawrence Somer
+	On Fermat d-pseudoprimes	1989	Lawrence Somer
+	Linear Recurrences Having Almost All Primes as Maximal Divisors	1986	Lawrence Somer
+	The divisibility and modular properties of KTH-order linear recurrences over the ring of integers of an algebraic number fields with respect of prime ideals	1985	Lawrence Somer
+	The Divisibility Properties of Primary Lucas Recurrences with Respect to Primes	1980	Lawrence Somer
+	The Fibonacci Ratios <i>F</i> <sub> <i>k</i> +1 </sub> / <i>F</i> <sub> <i>k</i> </sub> Modulo <i>p</i>	1975	Lawrence Somer
+	The Fibonacci Group and a new proof that F <sub>p−(5/p)</sub> ≡ 0 (mod p)	1972	Lawrence Somer

Common Coauthors

Coauthor	Papers Together
Michal Křı́žek	41
Florian Luca	18
Alena Šolcová	10
Walter Carlip	6
Eliot Jacobson	2
Guixin Deng	1
Jan Brandts	1
Peter Hilton	1
Lenny Jones	1
Jean Pedersen	1
Igor E. Shparlinski	1
Michal Křížek	1
Curtis Cooper	1
David Banks	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	On the Numerical Factors of the Arithmetic Forms α n ± β n	1913	R. D. Carmichael	14
+	An Extended Theory of Lucas' Functions	1930	D. H. Lehmer	11
+	Prime divisors of second order recurring sequences	1954	Morgan Ward	7
+	17 lectures on Fermat numbers : from number theory to geometry	2001	Michal Křı́žek Florian Luca Lawrence Somer Alena Šolcová	6
+	Theorie des Fonctions Numeriques Simplement Periodiques	1878	Édouard Lucas	6
+	The New Book of Prime Number Records	1996	Paulo Ribenboim	5
+	Applications of Fibonacci Numbers.	1989	C. T. Gray Ανδρέας Ν. Φιλίππου A. F. Horadam Gerald E. Bergum	5
+	An Introduction to the Theory of Numbers.	1961	W. J. LeVeque Ivan Niven Herbert S. Zuckerman	5
+	17 Lectures on Fermat Numbers	2001	Michal Křı́žek Florian Luca Lawrence Somer	5
+ PDF Chat	On a Connection of Number Theory with Graph Theory	2004	Lawrence Somer Michal Křı́žek	5
+ PDF Chat	Existence of primitive divisors of Lucas and Lehmer numbers	2001	Yonatan Bilu Guillaume Hanrot Paul Voutier	5
+	Divisibility of Terms in Lucas Sequences of the Second Kind by Their Subscripts	1996	Lawrence Somer	4
+	The divisibility and modular properties of KTH-order linear recurrences over the ring of integers of an algebraic number fields with respect of prime ideals	1985	Lawrence Somer	4
+ PDF Chat	On Numbers Analogous to the Carmichael Numbers	1977	Hywel C Williams	4
+ PDF Chat	Lucas pseudoprimes	1980	Robert Baillie Samuel S. Wagstaff	4
+ PDF Chat	Symmetry of iteration graphs	2008	Walter Carlip Martina Mincheva	4
+ PDF Chat	Unbounded stability of two-term recurrence sequences modulo $2^k$	1996	Walter Carlip Eliot Jacobson	3
+ PDF Chat	The intrinsic divisors of Lehmer numbers in the case of negative discriminant	1962	Andrzej Schinzel	3
+	The graph of the square mapping on the prime fields	1996	T. D. Rogers	3
+	On the Divisibility Properties of Fibonacci Numbers	1966	John H. Halton	3
+ PDF Chat	A lower bound for the counting function of Lucas pseudoprimes	1988	Péter L. Erdős Péter Kiss Andràs Sárközy	3
+ PDF Chat	An Introduction to the Theory of Numbers	1946	E. C. T.	3
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	3
+ PDF Chat	Frobenius pseudoprimes	2000	Jon Grantham	3
+ PDF Chat	A distribution property for linear recurrence of the second order	1975	Richard T. Bumby	3
+	On symmetric digraphs of the congruence <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si7.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msup><mml:mo>≡</mml:mo><mml:mi>y</mml:mi><mml:mspace width="0.16667em" /><mml:mrow><mml:mo>(</mml:mo><mml:mo>mod</mml:mo><mml:mspace width="0.334em" /><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>	2008	Lawrence Somer Michal Křı́žek	3
+	On the Determination of the Zeros of the Fibonacci Sequence	1966	Robert P. Backstrom	3
+	Structure of digraphs associated with quadratic congruences with composite moduli	2006	Lawrence Somer Michal Křı́žek	2
+ PDF Chat	The distribution of second order linear recurrence sequences mod $2^m$	1998	Mark Morgan	2
+	On the symmetric digraphs from powers modulo <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math>	2011	Guixin Deng Pingzhi Yuan	2
+	A Criterion For Stability of Two-Term Recurrence Sequences Modulo Odd Primes	1998	Walter Carlip Eliot Jacobson Lawrence Somer	2
+	Upper Bounds for Frequencies of Elements in Second-Order Recurrences over A Finite Field	1993	Lawrence Somer	2
+	On Lucasian Numbers	1997	Peter Hilton Jean Pedersen Lawrence Somer	2
+ PDF Chat	Note on a new number theory function	1910	R. D. Carmichael	2
+ PDF Chat	On the Diophantine equation $ax^{2t}+bx^ty+cy^2=d$ and pure powers in recurrence sequences.	1983	T. N. Shorey C. L. Stewart	2
+	Elementary Number Theory: Fourth Edition	1997	David Burton	2
+	The Fibonacci Matrix Modulo m	1963	Donald W. Robinson	2
+	Groups, Graphs, and Fermat's Last Theorem	1967	Steven Bryant	2
+	Possible Restricted Periods of Certain Lucas Sequences Modulo P	1991	Lawrence Somer	2
+	Arithmetical progressions formed by Lucas pseudoprimes	1998	A. Rotkiewicz	2
+	On Lucas pseudoprimes with a prescribed value of the Jacobi symbol	2000	A. Rotkiewicz Andrzej Schinzel	2
+	Applications d'un corps fini dans lui-même	1985	Guy Chassé	2
+ PDF Chat	On primitive prime factors of Lehmer numbers I	1963	Andrzej Schinzel	2
+ PDF Chat	Symmetric Digraphs from Powers Modulo &lt;i&gt;n&lt;/i&gt;	2011	Guixin Deng Pingzhi Yuan	2
+ PDF Chat	An introduction to the theory of numbers	1960	G. H. Hardy	2
+	On the quadratic character of some quadratic surds.	1971	Emma Lehmer	2
+	Combinatorial cycles of a polynomial map over a commutative field	1986	Guy Chassé	2
+ PDF Chat	Linear divisibility sequences	1937	Morgan Ward	1
+	The Most Beautiful Theorems on Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer	1
+	On the Convergence of Series of Reciprocals of Primes Related to the Fermat Numbers	2002	Michal Křı́žek Florian Luca Lawrence Somer	1