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## Somer, Lawrence E.

Compute Distance To:
 Author ID: somer.lawrence-e Published as: Somer, L.; Somer, Lawrence; Somer, Lawrence E.
 Documents Indexed: 97 Publications since 1972, including 3 Books
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#### Co-Authors

 38 single-authored 35 Křížek, Michal 11 Carlip, Walter 7 Luca, Florian 3 Jacobson, Eliot T. 3 Markl, Martin 2 Cooper, Curtis N. 2 Jones, Lenny K. 2 Kowalski, Oldřich 2 Pudlák, Pavel 2 Vrkoč, Ivo 1 Ahmad, Uzma 1 Banks, David C. 1 Carroll, Dana 1 Deng, Guixin 1 Hilton, Peter John 1 Husnine, Syed Muhammad 1 Katrnoška, František 1 Niederreiter, Harald 1 Parker, Ernest Tilden 1 Pedersen, Jean J. 1 Schinzel, Andrzej 1 Shparlinski, Igor E. 1 Šolcová, Alena
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#### Serials

 33 The Fibonacci Quarterly 6 Congressus Numerantium 5 Pokroky Matematiky, Fyziky & Astronomie 3 Czechoslovak Mathematical Journal 2 Discrete Mathematics 2 Commentationes Mathematicae Universitatis Carolinae 2 Mathematica Slovaca 2 Mathematica Bohemica 2 Integers 2 JP Journal of Algebra, Number Theory and Applications 1 Rocky Mountain Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Number Theory 1 Utilitas Mathematica 1 Elemente der Mathematik 1 Tatra Mountains Mathematical Publications 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 Journal of Integer Sequences 1 La Gaceta de la Real Sociedad Matemática Española 1 Gravitation & Cosmology 1 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1 Discrete Mathematics, Algorithms and Applications
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#### Fields

 88 Number theory (11-XX) 14 Combinatorics (05-XX) 7 History and biography (01-XX) 2 Group theory and generalizations (20-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Geometry (51-XX) 1 Numerical analysis (65-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)

#### Citations contained in zbMATH

44 Publications have been cited 152 times in 91 Documents Cited by Year
On a connection of number theory with graph theory. Zbl 1080.11004
Somer, Lawrence; Křížek, Michal
2004
On symmetric digraphs of the congruence $$x^k \equiv y \pmod n$$. Zbl 1208.05041
Somer, Lawrence; Křížek, Michal
2009
17 lectures on Fermat numbers. From number theory to geometry. With a foreword by Alena Šolcová. Zbl 1010.11002
Křížek, Michal; Luca, Florian; Somer, Lawrence
2001
Structure of digraphs associated with quadratic congruences with composite moduli. Zbl 1161.05323
Somer, Lawrence; Křížek, Michal
2006
Divisibility of terms in Lucas sequences by their subscripts. Zbl 0806.11013
Somer, Lawrence
1993
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
2002
The divisibility properties of primary Lucas recurrences with respect to primes. Zbl 0441.10007
Somer, Lawrence
1980
The structure of digraphs associated with the congruence $$x^k\equiv y \pmod n$$. Zbl 1249.11006
Somer, L.; Křížek, M.
2011
On symmetries of power digraphs. Zbl 1251.05066
Husnine, S. M.; Ahmad, Uzma; Somer, Lawrence
2011
On semiregular digraphs of the congruence $$x^k\equiv y\pmod n$$. Zbl 1174.05058
Somer, Lawrence; Křížek, Michal
2007
The residues of $$n^n$$ modulo $$p$$. Zbl 0451.10004
Somer, Lawrence
1981
A necessary and sufficient condition for the primality of Fermat numbers. Zbl 0993.11002
Křížek, Michal; Somer, Lawrence
2001
Distribution of two-term recurrence sequences mod $$p^ e$$. Zbl 0809.11011
Carroll, Dana; Jacobson, Eliot; Somer, Lawrence
1994
Maximal frequencies of elements in second-order linear recurring sequences over a finite field. Zbl 0747.11062
Niederreiter, H.; Schinzel, A.; Somer, L.
1991
Fibonacci-like groups and periods of Fibonacci-like sequences. Zbl 0364.10005
Somer, Lawrence
1977
On moduli for which certain second-order linear recurrences contain a complete system of residues modulo $$m$$. Zbl 1401.11049
Somer, Lawrence; Křížek, Michal
2017
Excessive extrapolations in cosmology. Zbl 1353.83034
Křížek, M.; Somer, L.
2016
On the symmetric digraphs from the $$k$$th power mapping on finite commutative rings. Zbl 1312.05061
Deng, Guixin; Somer, Lawrence
2015
Prime Lehmer and Lucas numbers with composite indices. Zbl 1291.11044
Somer, Lawrence; Křížek, Michal
2013
Second-order linear recurrences of composite numbers. Zbl 1161.11310
Somer, Lawrence
2006
Sophie Germain little suns. Zbl 1108.11002
Křížek, Michal; Somer, Lawrence
2004
Bounds for frequencies of residues of regular second-order recurrences modulo $$p^r$$. Zbl 0928.11010
Carlip, Walter; Somer, Lawrence
1999
Periodicity properties of $$k$$th order linear recurrences whose characteristic polynomial splits completely over a finite field. I. Zbl 0811.11015
Somer, Lawrence
1994
The Fibonacci group and a new proof that $$F_p-(5/p)\equiv 0$$ $$(mod \;p)$$. Zbl 0252.10010
Somer, Lawrence E.
1972
Nondefective integers with respect to certain Lucas sequences of the second kind. Zbl 1412.11025
Somer, Lawrence; Křížek, Michal
2018
Identically distributed second-order linear recurrences modulo $$p$$. Zbl 1397.11047
Somer, Lawrence; Křížek, Michal
2015
Why quintic polynomial equations are not solvable in radicals. Zbl 1374.12005
Křížek, Michal; Somer, Lawrence
2015
On the complexity of testing elite primes. Zbl 1226.11013
Křížek, Michal; Luca, Florian; Shparlinski, Igor E.; Somer, Lawrence
2011
Bounds for frequencies of residues of second-order recurrences modulo $$p^r$$. Zbl 1174.11014
Carlip, Walter; Somer, Lawrence
2007
Primitive Lucas $$d$$-pseudoprimes and Carmichael-Lucas numbers. Zbl 1187.11007
Carlip, Walter; Somer, Lawrence
2007
Stability classes of second-order linear recurrences modulo $$2^k$$. Zbl 0992.11013
Carlip, Walter; Somer, Lawrence
2000
Stability of second-order recurrences modulo $$p^r$$. Zbl 0979.11014
Somer, Lawrence; Carlip, Walter
2000
Pseudoprimes, perfect numbers, and a problem of Lehmer. Zbl 0934.11005
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1998
On Lucas $$d$$-pseudoprimes. Zbl 0919.11008
Somer, Lawrence
1998
A criterion for stability of two-term recurrence sequences modulo odd primes. Zbl 0921.11012
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1998
On Lucasian numbers. Zbl 0880.11020
Hilton, Peter; Pedersen, Jean; Somer, Lawrence
1997
Divisibility of terms in Lucas sequences of the second kind by their subscripts. Zbl 0861.11010
Somer, Lawrence
1996
Upper bounds for frequencies of elements in second-order recurrences over a finite field. Zbl 0805.11022
Somer, Lawrence
1993
Distribution of residues of certain second-order linear recurrences modulo p. II. Zbl 0728.11010
Somer, Lawrence
1991
Congruence relations for $$k^{th}$$-order linear recurrences. Zbl 0664.10003
Somer, Lawrence
1989
A partial generalization of Mann’s theorem concerning orthogonal Latin squares. Zbl 0669.05012
Parker, E. T.; Somer, Lawrence
1988
Primes having an incomplete system of residues for a class of second-order recurrences. Zbl 0653.10005
Somer, Lawrence
1988
Possible periods of primary Fibonacci-like sequences with respect to a fixed odd prime. Zbl 0498.10010
Somer, Lawrence
1982
Which second-order linear integral recurrences have almost all primes as divisors? Zbl 0401.10015
Somer, Lawrence
1979
Nondefective integers with respect to certain Lucas sequences of the second kind. Zbl 1412.11025
Somer, Lawrence; Křížek, Michal
2018
On moduli for which certain second-order linear recurrences contain a complete system of residues modulo $$m$$. Zbl 1401.11049
Somer, Lawrence; Křížek, Michal
2017
Excessive extrapolations in cosmology. Zbl 1353.83034
Křížek, M.; Somer, L.
2016
On the symmetric digraphs from the $$k$$th power mapping on finite commutative rings. Zbl 1312.05061
Deng, Guixin; Somer, Lawrence
2015
Identically distributed second-order linear recurrences modulo $$p$$. Zbl 1397.11047
Somer, Lawrence; Křížek, Michal
2015
Why quintic polynomial equations are not solvable in radicals. Zbl 1374.12005
Křížek, Michal; Somer, Lawrence
2015
Prime Lehmer and Lucas numbers with composite indices. Zbl 1291.11044
Somer, Lawrence; Křížek, Michal
2013
The structure of digraphs associated with the congruence $$x^k\equiv y \pmod n$$. Zbl 1249.11006
Somer, L.; Křížek, M.
2011
On symmetries of power digraphs. Zbl 1251.05066
Husnine, S. M.; Ahmad, Uzma; Somer, Lawrence
2011
On the complexity of testing elite primes. Zbl 1226.11013
Křížek, Michal; Luca, Florian; Shparlinski, Igor E.; Somer, Lawrence
2011
On symmetric digraphs of the congruence $$x^k \equiv y \pmod n$$. Zbl 1208.05041
Somer, Lawrence; Křížek, Michal
2009
On semiregular digraphs of the congruence $$x^k\equiv y\pmod n$$. Zbl 1174.05058
Somer, Lawrence; Křížek, Michal
2007
Bounds for frequencies of residues of second-order recurrences modulo $$p^r$$. Zbl 1174.11014
Carlip, Walter; Somer, Lawrence
2007
Primitive Lucas $$d$$-pseudoprimes and Carmichael-Lucas numbers. Zbl 1187.11007
Carlip, Walter; Somer, Lawrence
2007
Structure of digraphs associated with quadratic congruences with composite moduli. Zbl 1161.05323
Somer, Lawrence; Křížek, Michal
2006
Second-order linear recurrences of composite numbers. Zbl 1161.11310
Somer, Lawrence
2006
On a connection of number theory with graph theory. Zbl 1080.11004
Somer, Lawrence; Křížek, Michal
2004
Sophie Germain little suns. Zbl 1108.11002
Křížek, Michal; Somer, Lawrence
2004
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
2002
17 lectures on Fermat numbers. From number theory to geometry. With a foreword by Alena Šolcová. Zbl 1010.11002
Křížek, Michal; Luca, Florian; Somer, Lawrence
2001
A necessary and sufficient condition for the primality of Fermat numbers. Zbl 0993.11002
Křížek, Michal; Somer, Lawrence
2001
Stability classes of second-order linear recurrences modulo $$2^k$$. Zbl 0992.11013
Carlip, Walter; Somer, Lawrence
2000
Stability of second-order recurrences modulo $$p^r$$. Zbl 0979.11014
Somer, Lawrence; Carlip, Walter
2000
Bounds for frequencies of residues of regular second-order recurrences modulo $$p^r$$. Zbl 0928.11010
Carlip, Walter; Somer, Lawrence
1999
Pseudoprimes, perfect numbers, and a problem of Lehmer. Zbl 0934.11005
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1998
On Lucas $$d$$-pseudoprimes. Zbl 0919.11008
Somer, Lawrence
1998
A criterion for stability of two-term recurrence sequences modulo odd primes. Zbl 0921.11012
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1998
On Lucasian numbers. Zbl 0880.11020
Hilton, Peter; Pedersen, Jean; Somer, Lawrence
1997
Divisibility of terms in Lucas sequences of the second kind by their subscripts. Zbl 0861.11010
Somer, Lawrence
1996
Distribution of two-term recurrence sequences mod $$p^ e$$. Zbl 0809.11011
Carroll, Dana; Jacobson, Eliot; Somer, Lawrence
1994
Periodicity properties of $$k$$th order linear recurrences whose characteristic polynomial splits completely over a finite field. I. Zbl 0811.11015
Somer, Lawrence
1994
Divisibility of terms in Lucas sequences by their subscripts. Zbl 0806.11013
Somer, Lawrence
1993
Upper bounds for frequencies of elements in second-order recurrences over a finite field. Zbl 0805.11022
Somer, Lawrence
1993
Maximal frequencies of elements in second-order linear recurring sequences over a finite field. Zbl 0747.11062
Niederreiter, H.; Schinzel, A.; Somer, L.
1991
Distribution of residues of certain second-order linear recurrences modulo p. II. Zbl 0728.11010
Somer, Lawrence
1991
Congruence relations for $$k^{th}$$-order linear recurrences. Zbl 0664.10003
Somer, Lawrence
1989
A partial generalization of Mann’s theorem concerning orthogonal Latin squares. Zbl 0669.05012
Parker, E. T.; Somer, Lawrence
1988
Primes having an incomplete system of residues for a class of second-order recurrences. Zbl 0653.10005
Somer, Lawrence
1988
Possible periods of primary Fibonacci-like sequences with respect to a fixed odd prime. Zbl 0498.10010
Somer, Lawrence
1982
The residues of $$n^n$$ modulo $$p$$. Zbl 0451.10004
Somer, Lawrence
1981
The divisibility properties of primary Lucas recurrences with respect to primes. Zbl 0441.10007
Somer, Lawrence
1980
Which second-order linear integral recurrences have almost all primes as divisors? Zbl 0401.10015
Somer, Lawrence
1979
Fibonacci-like groups and periods of Fibonacci-like sequences. Zbl 0364.10005
Somer, Lawrence
1977
The Fibonacci group and a new proof that $$F_p-(5/p)\equiv 0$$ $$(mod \;p)$$. Zbl 0252.10010
Somer, Lawrence E.
1972
all top 5

#### Cited by 101 Authors

 14 Czechoslovak Mathematical Journal 8 Finite Fields and their Applications 7 Journal of Number Theory 5 International Journal of Number Theory 4 Discrete Mathematics 3 Mathematics of Computation 3 Proceedings of the American Mathematical Society 3 Journal of Integer Sequences 3 Integers 3 Gravitation & Cosmology 3 Journal of Algebra and its Applications 3 Discrete Mathematics, Algorithms and Applications 2 Rocky Mountain Journal of Mathematics 2 Applied Mathematics and Computation 2 Mathematica Slovaca 2 Algebra Colloquium 2 The New York Journal of Mathematics 1 Bulletin of the Australian Mathematical Society 1 Discrete Applied Mathematics 1 Information Processing Letters 1 The Mathematical Intelligencer 1 Functiones et Approximatio. Commentarii Mathematici 1 Journal of Combinatorial Theory. Series B 1 Journal of Pure and Applied Algebra 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Programming and Computer Software 1 Advances in Applied Mathematics 1 Indagationes Mathematicae. New Series 1 Journal de Théorie des Nombres de Bordeaux 1 Turkish Journal of Mathematics 1 Acta Mathematica et Informatica Universitatis Ostraviensis 1 Analysis (München) 1 Acta Mathematica Sinica. English Series 1 Journal of Applied Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 1 Journal of Applied Analysis and Computation 1 Journal of Mathematics 1 Cogent Mathematics & Statistics