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Somer, Lawrence E.

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Author ID: somer.lawrence-e Recent zbMATH articles by "Somer, Lawrence E."
Published as: Somer, L.; Somer, Lawrence; Somer, Lawrence E.
Documents Indexed: 97 Publications since 1972, including 3 Books

Publications by Year

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
24
2004
On symmetric digraphs of the congruence \(x^k \equiv y \pmod n\). Zbl 1208.05041
Somer, Lawrence; Křížek, Michal
14
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
14
2001
Structure of digraphs associated with quadratic congruences with composite moduli. Zbl 1161.05323
Somer, Lawrence; Křížek, Michal
12
2006
Divisibility of terms in Lucas sequences by their subscripts. Zbl 0806.11013
Somer, Lawrence
9
1993
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
6
2002
The divisibility properties of primary Lucas recurrences with respect to primes. Zbl 0441.10007
Somer, Lawrence
6
1980
The structure of digraphs associated with the congruence \(x^k\equiv y \pmod n\). Zbl 1249.11006
Somer, L.; Křížek, M.
5
2011
On symmetries of power digraphs. Zbl 1251.05066
Husnine, S. M.; Ahmad, Uzma; Somer, Lawrence
4
2011
On semiregular digraphs of the congruence \(x^k\equiv y\pmod n\). Zbl 1174.05058
Somer, Lawrence; Křížek, Michal
4
2007
The residues of \(n^n\) modulo \(p\). Zbl 0451.10004
Somer, Lawrence
4
1981
A necessary and sufficient condition for the primality of Fermat numbers. Zbl 0993.11002
Křížek, Michal; Somer, Lawrence
3
2001
Distribution of two-term recurrence sequences mod \(p^ e\). Zbl 0809.11011
Carroll, Dana; Jacobson, Eliot; Somer, Lawrence
3
1994
Maximal frequencies of elements in second-order linear recurring sequences over a finite field. Zbl 0747.11062
Niederreiter, H.; Schinzel, A.; Somer, L.
3
1991
Fibonacci-like groups and periods of Fibonacci-like sequences. Zbl 0364.10005
Somer, Lawrence
3
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
2
2017
Excessive extrapolations in cosmology. Zbl 1353.83034
Křížek, M.; Somer, L.
2
2016
On the symmetric digraphs from the \(k\)th power mapping on finite commutative rings. Zbl 1312.05061
Deng, Guixin; Somer, Lawrence
2
2015
Prime Lehmer and Lucas numbers with composite indices. Zbl 1291.11044
Somer, Lawrence; Křížek, Michal
2
2013
Second-order linear recurrences of composite numbers. Zbl 1161.11310
Somer, Lawrence
2
2006
Sophie Germain little suns. Zbl 1108.11002
Křížek, Michal; Somer, Lawrence
2
2004
Bounds for frequencies of residues of regular second-order recurrences modulo \(p^r\). Zbl 0928.11010
Carlip, Walter; Somer, Lawrence
2
1999
Periodicity properties of \(k\)th order linear recurrences whose characteristic polynomial splits completely over a finite field. I. Zbl 0811.11015
Somer, Lawrence
2
1994
The Fibonacci group and a new proof that \(F_p-(5/p)\equiv 0\) \((mod \;p)\). Zbl 0252.10010
Somer, Lawrence E.
2
1972
Nondefective integers with respect to certain Lucas sequences of the second kind. Zbl 1412.11025
Somer, Lawrence; Křížek, Michal
1
2018
Identically distributed second-order linear recurrences modulo \(p\). Zbl 1397.11047
Somer, Lawrence; Křížek, Michal
1
2015
Why quintic polynomial equations are not solvable in radicals. Zbl 1374.12005
Křížek, Michal; Somer, Lawrence
1
2015
On the complexity of testing elite primes. Zbl 1226.11013
Křížek, Michal; Luca, Florian; Shparlinski, Igor E.; Somer, Lawrence
1
2011
Bounds for frequencies of residues of second-order recurrences modulo \(p^r\). Zbl 1174.11014
Carlip, Walter; Somer, Lawrence
1
2007
Primitive Lucas \(d\)-pseudoprimes and Carmichael-Lucas numbers. Zbl 1187.11007
Carlip, Walter; Somer, Lawrence
1
2007
Stability classes of second-order linear recurrences modulo \(2^k\). Zbl 0992.11013
Carlip, Walter; Somer, Lawrence
1
2000
Stability of second-order recurrences modulo \(p^r\). Zbl 0979.11014
Somer, Lawrence; Carlip, Walter
1
2000
Pseudoprimes, perfect numbers, and a problem of Lehmer. Zbl 0934.11005
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1
1998
On Lucas \(d\)-pseudoprimes. Zbl 0919.11008
Somer, Lawrence
1
1998
A criterion for stability of two-term recurrence sequences modulo odd primes. Zbl 0921.11012
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1
1998
On Lucasian numbers. Zbl 0880.11020
Hilton, Peter; Pedersen, Jean; Somer, Lawrence
1
1997
Divisibility of terms in Lucas sequences of the second kind by their subscripts. Zbl 0861.11010
Somer, Lawrence
1
1996
Upper bounds for frequencies of elements in second-order recurrences over a finite field. Zbl 0805.11022
Somer, Lawrence
1
1993
Distribution of residues of certain second-order linear recurrences modulo p. II. Zbl 0728.11010
Somer, Lawrence
1
1991
Congruence relations for \(k^{th}\)-order linear recurrences. Zbl 0664.10003
Somer, Lawrence
1
1989
A partial generalization of Mann’s theorem concerning orthogonal Latin squares. Zbl 0669.05012
Parker, E. T.; Somer, Lawrence
1
1988
Primes having an incomplete system of residues for a class of second-order recurrences. Zbl 0653.10005
Somer, Lawrence
1
1988
Possible periods of primary Fibonacci-like sequences with respect to a fixed odd prime. Zbl 0498.10010
Somer, Lawrence
1
1982
Which second-order linear integral recurrences have almost all primes as divisors? Zbl 0401.10015
Somer, Lawrence
1
1979
Nondefective integers with respect to certain Lucas sequences of the second kind. Zbl 1412.11025
Somer, Lawrence; Křížek, Michal
1
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
2
2017
Excessive extrapolations in cosmology. Zbl 1353.83034
Křížek, M.; Somer, L.
2
2016
On the symmetric digraphs from the \(k\)th power mapping on finite commutative rings. Zbl 1312.05061
Deng, Guixin; Somer, Lawrence
2
2015
Identically distributed second-order linear recurrences modulo \(p\). Zbl 1397.11047
Somer, Lawrence; Křížek, Michal
1
2015
Why quintic polynomial equations are not solvable in radicals. Zbl 1374.12005
Křížek, Michal; Somer, Lawrence
1
2015
Prime Lehmer and Lucas numbers with composite indices. Zbl 1291.11044
Somer, Lawrence; Křížek, Michal
2
2013
The structure of digraphs associated with the congruence \(x^k\equiv y \pmod n\). Zbl 1249.11006
Somer, L.; Křížek, M.
5
2011
On symmetries of power digraphs. Zbl 1251.05066
Husnine, S. M.; Ahmad, Uzma; Somer, Lawrence
4
2011
On the complexity of testing elite primes. Zbl 1226.11013
Křížek, Michal; Luca, Florian; Shparlinski, Igor E.; Somer, Lawrence
1
2011
On symmetric digraphs of the congruence \(x^k \equiv y \pmod n\). Zbl 1208.05041
Somer, Lawrence; Křížek, Michal
14
2009
On semiregular digraphs of the congruence \(x^k\equiv y\pmod n\). Zbl 1174.05058
Somer, Lawrence; Křížek, Michal
4
2007
Bounds for frequencies of residues of second-order recurrences modulo \(p^r\). Zbl 1174.11014
Carlip, Walter; Somer, Lawrence
1
2007
Primitive Lucas \(d\)-pseudoprimes and Carmichael-Lucas numbers. Zbl 1187.11007
Carlip, Walter; Somer, Lawrence
1
2007
Structure of digraphs associated with quadratic congruences with composite moduli. Zbl 1161.05323
Somer, Lawrence; Křížek, Michal
12
2006
Second-order linear recurrences of composite numbers. Zbl 1161.11310
Somer, Lawrence
2
2006
On a connection of number theory with graph theory. Zbl 1080.11004
Somer, Lawrence; Křížek, Michal
24
2004
Sophie Germain little suns. Zbl 1108.11002
Křížek, Michal; Somer, Lawrence
2
2004
On the convergence of series of reciprocals of primes related to the Fermat numbers. Zbl 1026.11011
Křížek, Michal; Luca, Florian; Somer, Lawrence
6
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
14
2001
A necessary and sufficient condition for the primality of Fermat numbers. Zbl 0993.11002
Křížek, Michal; Somer, Lawrence
3
2001
Stability classes of second-order linear recurrences modulo \(2^k\). Zbl 0992.11013
Carlip, Walter; Somer, Lawrence
1
2000
Stability of second-order recurrences modulo \(p^r\). Zbl 0979.11014
Somer, Lawrence; Carlip, Walter
1
2000
Bounds for frequencies of residues of regular second-order recurrences modulo \(p^r\). Zbl 0928.11010
Carlip, Walter; Somer, Lawrence
2
1999
Pseudoprimes, perfect numbers, and a problem of Lehmer. Zbl 0934.11005
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1
1998
On Lucas \(d\)-pseudoprimes. Zbl 0919.11008
Somer, Lawrence
1
1998
A criterion for stability of two-term recurrence sequences modulo odd primes. Zbl 0921.11012
Carlip, Walter; Jacobson, Eliot; Somer, Lawrence
1
1998
On Lucasian numbers. Zbl 0880.11020
Hilton, Peter; Pedersen, Jean; Somer, Lawrence
1
1997
Divisibility of terms in Lucas sequences of the second kind by their subscripts. Zbl 0861.11010
Somer, Lawrence
1
1996
Distribution of two-term recurrence sequences mod \(p^ e\). Zbl 0809.11011
Carroll, Dana; Jacobson, Eliot; Somer, Lawrence
3
1994
Periodicity properties of \(k\)th order linear recurrences whose characteristic polynomial splits completely over a finite field. I. Zbl 0811.11015
Somer, Lawrence
2
1994
Divisibility of terms in Lucas sequences by their subscripts. Zbl 0806.11013
Somer, Lawrence
9
1993
Upper bounds for frequencies of elements in second-order recurrences over a finite field. Zbl 0805.11022
Somer, Lawrence
1
1993
Maximal frequencies of elements in second-order linear recurring sequences over a finite field. Zbl 0747.11062
Niederreiter, H.; Schinzel, A.; Somer, L.
3
1991
Distribution of residues of certain second-order linear recurrences modulo p. II. Zbl 0728.11010
Somer, Lawrence
1
1991
Congruence relations for \(k^{th}\)-order linear recurrences. Zbl 0664.10003
Somer, Lawrence
1
1989
A partial generalization of Mann’s theorem concerning orthogonal Latin squares. Zbl 0669.05012
Parker, E. T.; Somer, Lawrence
1
1988
Primes having an incomplete system of residues for a class of second-order recurrences. Zbl 0653.10005
Somer, Lawrence
1
1988
Possible periods of primary Fibonacci-like sequences with respect to a fixed odd prime. Zbl 0498.10010
Somer, Lawrence
1
1982
The residues of \(n^n\) modulo \(p\). Zbl 0451.10004
Somer, Lawrence
4
1981
The divisibility properties of primary Lucas recurrences with respect to primes. Zbl 0441.10007
Somer, Lawrence
6
1980
Which second-order linear integral recurrences have almost all primes as divisors? Zbl 0401.10015
Somer, Lawrence
1
1979
Fibonacci-like groups and periods of Fibonacci-like sequences. Zbl 0364.10005
Somer, Lawrence
3
1977
The Fibonacci group and a new proof that \(F_p-(5/p)\equiv 0\) \((mod \;p)\). Zbl 0252.10010
Somer, Lawrence E.
2
1972
all top 5

Cited by 101 Authors

14 Somer, Lawrence E.
10 Křížek, Michal
9 Sanna, Carlo
6 Deng, Guixin
5 Wei, Yangjiang
4 Ahmad, Uzma
4 Brison, Owen J.
4 Meemark, Yotsanan
4 Nogueira, Joaquim Eurico
4 Tang, Gaohua
3 Carlip, Walter
3 Dubickas, Artūras
3 Jones, Lenny K.
3 Nan, Jizhu
3 Yuan, Pingzhi
2 Harrington, Joshua
2 Just, Matthew
2 Luca, Florian
2 Moeen, Muqadas
2 Müller, Tom
2 Novikas, Aivaras
2 Sawkmie, Amplify
2 Singh, Madan Mohan
2 Skowronek-Kaziów, Joanna
2 Wiroonsri, Nathakhun
2 Witno, Amin
2 Zhao, Jinxing
1 Anghel, Catalina V.
1 Barańczuk, Stefan
1 Benedito, Cintya Wink de Oliveira
1 Carmelo Interlando, J.
1 Castro, Francis Noel
1 Chathurika, Amarasingha Arachchige Mihiri
1 Chaumont, Alain
1 Cilleruelo, Javier
1 Cosgrave, John B.
1 Dilcher, Karl
1 Dumin, Yu. V.
1 Fan, Shilei
1 Felix, Adam Tyler
1 Garaev, Moubariz Z.
1 Grau, José María
1 Hardy, Michael
1 Herendi, Tamás
1 Hindes, Wade
1 Holden, Joshua Brandon
1 Hone, Andrew N. W.
1 Hou, Qinghu
1 Ismailescu, Dan P.
1 Jaroma, John H.
1 Jeffery, L. Edson
1 Jiang, Xiaoyu
1 Jiang, Zhaolin
1 Ju, Tengxia
1 Karaduman, Erdal
1 Ko, Adrienne
1 Konyagin, Sergeĭ Vladimirovich
1 Kurlberg, Pär
1 Lee, Celine
1 Leicht, Johannes
1 Leonetti, Paolo
1 Liang, Linhua
1 Liang, Mingxuan
1 Liao, Lingmin
1 Liu, Tiejun
1 Mahmood, Muhammad Khalid
1 Maingam, Nawaphon
1 Malik, M. Aslam
1 Mans, Bernard
1 Mastrostefano, Daniele
1 Mathieson, Luke
1 Medina, Luis A.
1 Mincheva, Martina
1 Mu, Yanping
1 Murru, Nadir
1 Oller-Marcén, Antonio M.
1 Özkan, Engin
1 Palazzo, Reginaldo jun.
1 Park, Jae-Yong
1 Pollack, Paul
1 Pongsriiam, Prapanpong
1 Reinhart, Andreas
1 Richardson, Pamela A.
1 Robinson, Margaret M.
1 Rout, Sudhansu Sekhar
1 Selcoe, Robert G.
1 Sha, Min
1 Shon, Sugoog
1 Shparlinski, Igor E.
1 Stewart, Andrew M.
1 Su, Huadong
1 Syed, Husnine
1 Tiwari, Bhupendra Nath
1 Tocharoenirattisai, Ittiwat
1 Tron, Emanuele
1 Wei, Yunlan
1 Woodgold, Catherine
1 Wu, Meiyun
1 Xu, Heyan
1 Yavuz, Uǧur
...and 1 more Authors
all top 5

Cited in 39 Serials

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

Citations by Year