John Brillhart - Author Profile

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Brillhart, John (b. 1930 d. 2022)

Author ID:	brillhart.john
Published as:	Brillhart, John; Brillhart, J.
Further Spellings:	Brillhart, John David
External Links:	MGP · Wikidata · GND · IdRef

Documents Indexed:	60 Publications since 1960, including 3 Books
	1 Further Contribution
Co-Authors:	24 Co-Authors with 36 Joint Publications
	839 Co-Co-Authors

all top 5

Co-Authors

23	single-authored
14	Blecksmith, Richard
10	Gerst, Irving
5	Morton, Patrick
4	Lehmer, Derrick Henry
4	Selfridge, John L.
2	Apel, Geoffrey
2	Decaro, Michael
2	Lomont, John S.
2	Morrison, Michael A.
2	Tuckerman, Bryant
2	Wagstaff, Samuel Standfield jun.
2	Zierler, Neal
1	Brawley, Joel Vincent jun.
1	Carlitz, Leonard
1	Erdős, Pál
1	Filaseta, Michael A.
1	Gould, Henry Wadsworth
1	Hallyburton, John C. jun.
1	Jarden, Dov
1	Montgomery, Peter Lawrence
1	Odlyzko, Andrew M.
1	Silverman, Robert D.
1	Tonascia, James
1	Trotskaia Lehmer, Emma
1	Weinberger, Peter J.

all top 5

Serials

20	Mathematics of Computation
5	American Mathematical Monthly
3	Rocky Mountain Journal of Mathematics
3	Acta Arithmetica
3	Pacific Journal of Mathematics
2	Information and Control
2	Journal of Number Theory
2	Journal für die Reine und Angewandte Mathematik
2	Notices of the American Mathematical Society
2	Bulletin of the Institute of Combinatorics and its Applications
2	Contemporary Mathematics
1	Canadian Journal of Mathematics
1	Duke Mathematical Journal
1	The Fibonacci Quarterly
1	Illinois Journal of Mathematics
1	Proceedings of the American Mathematical Society
1	Utilitas Mathematica
1	Integers
1	Bulletin of the American Mathematical Society

all top 5

Fields

43	Number theory (11-XX)
10	Combinatorics (05-XX)
6	History and biography (01-XX)
4	Special functions (33-XX)
4	Numerical analysis (65-XX)
3	Field theory and polynomials (12-XX)
3	Computer science (68-XX)
1	General and overarching topics; collections (00-XX)
1	Algebraic geometry (14-XX)
1	Linear and multilinear algebra; matrix theory (15-XX)
1	Real functions (26-XX)
1	Mathematics education (97-XX)

Publications by Year

all cited Publications top 5 cited Publications

Citations contained in zbMATH Open

44 Publications have been cited 477 times in 367 Documents	Cited by ▼	Year ▼
New primality criteria and factorizations of \(2^m\pm 1\). Zbl 0311.10009 Brillhart, John; Lehmer, D. H.; Selfridge, J. L.	43	1975
Factorizations of \(b^ n\pm 1\), \(b=2,3,5,6,7,10,11,12\) up to high powers. 2nd ed. Zbl 0659.10001 Brillhart, John; Lehmer, D. H.; Selfridge, J. L.; Tuckerman, Bryant; Wagstaff, S. S. jun.	38	1988
A method of factoring and the factorization of \(F_7\). Zbl 0302.10010 Morrison, Michael A.; Brillhart, John	37	1975
Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial. Zbl 1083.11036 Brillhart, John; Morton, Patrick	31	2004
Factorizations of \(b^n\pm 1\), \(b=2,3,5,6,7,10,11,12\) up to high powers. Zbl 0527.10001 Brillhart, John; Lehmer, D. H.; Selfridge, J. L.; Tuckerman, Bryant; Wagstaff, S. S. jun.	30	1983
On the Euler and Bernoulli polynomials. Zbl 0167.35401 Brillhart, John	20	1969
On the Fermat quotient. Zbl 0217.03203 Brillhart, J.; Tonascia, J.; Weinberger, P.	18	1971
Some infinite product identities. Zbl 0655.10010 Blecksmith, Richard; Brillhart, John; Gerst, Irving	16	1988
On primitive trinomials (mod 2). Zbl 0165.06503 Zierler, N.; Brillhart, J.	16	1968
Note on the Shapiro polynomials. Zbl 0191.35101 Brillhart, J.; Carlitz, Leonard	15	1970
Parity results for certain partition functions and identities similar to theta function identities. Zbl 0617.10010 Blecksmith, Richard; Brillhart, John; Gerst, Irving	14	1987
On sums of Rudin-Shapiro coefficients. II. Zbl 0469.10034 Brillhart, John; Erdős, Paul; Morton, Patrick	14	1983
On primitive trinomials (mod 2). II. Zbl 0184.07705 Zierler, Neal; Brillhart, John	14	1969
On the prime divisors of polynomials. Zbl 0214.30604 Gerst, I.; Brillhart, J.	13	1971
Über Summen von Rudin-Shapiroschen Koeffizienten. Zbl 0371.10009 Brillhart, John; Morton, Patrick	13	1978
On an irreducibility theorem of A. Cohn. Zbl 0481.12006 Brillhart, John; Filaseta, Michael; Odlyzko, Andrew	11	1981
Some factorizations of \(2^n\pm 1\) and related results. Zbl 0146.04903 Brillhart, John; Selfridge, J. L.	11	1967
Note on representing a prime as a sum of two squares. Zbl 0259.10006 Brillhart, John	11	1972
Cyclotomic properties of the Rudin-Shapiro polynomials. Zbl 0335.12003 Brillhart, John; Lomont, J. S.; Morton, Patrick	10	1976
On the Rudin-Shapiro polynomials. Zbl 0263.33012 Brillhart, John	9	1973
Tables of Fibonacci and Lucas factorizations. Zbl 0634.10002 Brillhart, John; Montgomery, Peter L.; Silverman, Robert D.	8	1988
A case study in mathematical research: The Golay-Rudin-Shapiro sequence. Zbl 0873.11020 Brillhart, John; Morton, Patrick	8	1996
Bound for pairs of consecutive seventh and higher power residues. Zbl 0124.27901 Brillhart, John; Lehmer, D. H.; Lehmer, Emma	8	1964
Note on the single variable Bell polynomials. Zbl 0152.02304 Brillhart, J.	8	1967
Two new factors of Fermat numbers. Zbl 0297.10001 Hallyburton, John C. jun.; Brillhart, John	7	1975
Some miscellaneous factorizations. Zbl 0115.26301 Brillhart, J.	7	1963
Elliptic polynomials. Zbl 0962.33001 Lomont, J. S.; Brillhart, John	6	2001
A fundamental modular identity and some applications. Zbl 0790.05011 Blecksmith, Richard; Brillhart, John; Gerst, Irving	6	1993
On the factors of certain Mersenne numbers. Zbl 0099.26305 Brillhart, John; Johnson, G. D.	6	1960
The factorization of \(F_7\). Zbl 0302.10009 Morrison, Michael A.; Brillhart, John	5	1971
On a certain (mod 2) identity and a method of proof by expansion. Zbl 0724.05004 Blecksmith, Richard; Brillhart, John; Gerst, Irving	4	1991
New proofs for two infinite product identities. Zbl 0767.11048 Blecksmith, Richard; Brillhart, John; Gerst, Irving	3	1992
On the factors of certain Mersenne numbers. II. Zbl 0118.04603 Brillhart, John	3	1964
A computer-assisted investigation of Ramanujan pairs. Zbl 0586.10008 Blecksmith, Richard; Brillhart, John; Gerst, Irving	3	1986
Recurring sequences. A collection of papers. Including numerous new factorizations of Fibonacci and Lucas numbers by John Brillhart. 2nd revised and enlarged edition. Zbl 1428.11004 Jarden, Dov	2	1966
Derrick Henry Lehmer. Zbl 0774.11003 Brillhart, John	2	1992
Fermat’s factoring method and its variants. Zbl 0488.10006 Brillhart, John	2	1981
A note on Euler’s factoring problem. Zbl 1229.11015 Brillhart, John	1	2009
A constructive theory of triple and quintuple product identities of the second degree. Zbl 0941.05007 Blecksmith, Richard; Brillhart, John; Gerst, Irving	1	1998
Concerning the numbers \(2^{2p}+1\), \(p\) prime. Zbl 0105.03202 Brillhart, John	1	1963
Note on irreducibility testing. Zbl 0451.12012 Brillhart, John	1	1980
Note on Fibonacci primality testing. Zbl 0946.11003 Brillhart, John	1	1998
Some modular results on the Euler and Bernoulli polynomials. Zbl 0213.05503 Brillhart, John	1	1972
Commentary on Lucas’ test. Zbl 1093.11002 Brillhart, John	1	2004
A note on Euler’s factoring problem. Zbl 1229.11015 Brillhart, John	1	2009
Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial. Zbl 1083.11036 Brillhart, John; Morton, Patrick	31	2004
Commentary on Lucas’ test. Zbl 1093.11002 Brillhart, John	1	2004
Elliptic polynomials. Zbl 0962.33001 Lomont, J. S.; Brillhart, John	6	2001
A constructive theory of triple and quintuple product identities of the second degree. Zbl 0941.05007 Blecksmith, Richard; Brillhart, John; Gerst, Irving	1	1998
Note on Fibonacci primality testing. Zbl 0946.11003 Brillhart, John	1	1998
A case study in mathematical research: The Golay-Rudin-Shapiro sequence. Zbl 0873.11020 Brillhart, John; Morton, Patrick	8	1996
A fundamental modular identity and some applications. Zbl 0790.05011 Blecksmith, Richard; Brillhart, John; Gerst, Irving	6	1993
New proofs for two infinite product identities. Zbl 0767.11048 Blecksmith, Richard; Brillhart, John; Gerst, Irving	3	1992
Derrick Henry Lehmer. Zbl 0774.11003 Brillhart, John	2	1992
On a certain (mod 2) identity and a method of proof by expansion. Zbl 0724.05004 Blecksmith, Richard; Brillhart, John; Gerst, Irving	4	1991
Factorizations of \(b^ n\pm 1\), \(b=2,3,5,6,7,10,11,12\) up to high powers. 2nd ed. Zbl 0659.10001 Brillhart, John; Lehmer, D. H.; Selfridge, J. L.; Tuckerman, Bryant; Wagstaff, S. S. jun.	38	1988
Some infinite product identities. Zbl 0655.10010 Blecksmith, Richard; Brillhart, John; Gerst, Irving	16	1988
Tables of Fibonacci and Lucas factorizations. Zbl 0634.10002 Brillhart, John; Montgomery, Peter L.; Silverman, Robert D.	8	1988
Parity results for certain partition functions and identities similar to theta function identities. Zbl 0617.10010 Blecksmith, Richard; Brillhart, John; Gerst, Irving	14	1987
A computer-assisted investigation of Ramanujan pairs. Zbl 0586.10008 Blecksmith, Richard; Brillhart, John; Gerst, Irving	3	1986
Factorizations of \(b^n\pm 1\), \(b=2,3,5,6,7,10,11,12\) up to high powers. Zbl 0527.10001 Brillhart, John; Lehmer, D. H.; Selfridge, J. L.; Tuckerman, Bryant; Wagstaff, S. S. jun.	30	1983
On sums of Rudin-Shapiro coefficients. II. Zbl 0469.10034 Brillhart, John; Erdős, Paul; Morton, Patrick	14	1983
On an irreducibility theorem of A. Cohn. Zbl 0481.12006 Brillhart, John; Filaseta, Michael; Odlyzko, Andrew	11	1981
Fermat’s factoring method and its variants. Zbl 0488.10006 Brillhart, John	2	1981
Note on irreducibility testing. Zbl 0451.12012 Brillhart, John	1	1980
Über Summen von Rudin-Shapiroschen Koeffizienten. Zbl 0371.10009 Brillhart, John; Morton, Patrick	13	1978
Cyclotomic properties of the Rudin-Shapiro polynomials. Zbl 0335.12003 Brillhart, John; Lomont, J. S.; Morton, Patrick	10	1976
New primality criteria and factorizations of \(2^m\pm 1\). Zbl 0311.10009 Brillhart, John; Lehmer, D. H.; Selfridge, J. L.	43	1975
A method of factoring and the factorization of \(F_7\). Zbl 0302.10010 Morrison, Michael A.; Brillhart, John	37	1975
Two new factors of Fermat numbers. Zbl 0297.10001 Hallyburton, John C. jun.; Brillhart, John	7	1975
On the Rudin-Shapiro polynomials. Zbl 0263.33012 Brillhart, John	9	1973
Note on representing a prime as a sum of two squares. Zbl 0259.10006 Brillhart, John	11	1972
Some modular results on the Euler and Bernoulli polynomials. Zbl 0213.05503 Brillhart, John	1	1972
On the Fermat quotient. Zbl 0217.03203 Brillhart, J.; Tonascia, J.; Weinberger, P.	18	1971
On the prime divisors of polynomials. Zbl 0214.30604 Gerst, I.; Brillhart, J.	13	1971
The factorization of \(F_7\). Zbl 0302.10009 Morrison, Michael A.; Brillhart, John	5	1971
Note on the Shapiro polynomials. Zbl 0191.35101 Brillhart, J.; Carlitz, Leonard	15	1970
On the Euler and Bernoulli polynomials. Zbl 0167.35401 Brillhart, John	20	1969
On primitive trinomials (mod 2). II. Zbl 0184.07705 Zierler, Neal; Brillhart, John	14	1969
On primitive trinomials (mod 2). Zbl 0165.06503 Zierler, N.; Brillhart, J.	16	1968
Some factorizations of \(2^n\pm 1\) and related results. Zbl 0146.04903 Brillhart, John; Selfridge, J. L.	11	1967
Note on the single variable Bell polynomials. Zbl 0152.02304 Brillhart, J.	8	1967
Recurring sequences. A collection of papers. Including numerous new factorizations of Fibonacci and Lucas numbers by John Brillhart. 2nd revised and enlarged edition. Zbl 1428.11004 Jarden, Dov	2	1966
Bound for pairs of consecutive seventh and higher power residues. Zbl 0124.27901 Brillhart, John; Lehmer, D. H.; Lehmer, Emma	8	1964
On the factors of certain Mersenne numbers. II. Zbl 0118.04603 Brillhart, John	3	1964
Some miscellaneous factorizations. Zbl 0115.26301 Brillhart, J.	7	1963
Concerning the numbers \(2^{2p}+1\), \(p\) prime. Zbl 0105.03202 Brillhart, John	1	1963
On the factors of certain Mersenne numbers. Zbl 0099.26305 Brillhart, John; Johnson, G. D.	6	1960

all cited Publications top 5 cited Publications

all top 5

Cited by 461 Authors

11	Brent, Richard Peirce
11	Brillhart, John
11	Morton, Patrick
9	Williams, Hugh Cowie
7	Blecksmith, Richard
7	Wagstaff, Samuel Standfield jun.
6	Dubner, Harvey
6	Erdélyi, Tamás
5	Cullinan, John
5	Filaseta, Michael A.
5	Gerst, Irving
5	Morain, François
4	Keller, Wilfrid
4	Kim, Taekyun
4	von zur Gathen, Joachim
3	Bazsó, András
3	Bonciocat, Nicolae Ciprian
3	Buchmann, Johannes A.
3	Cooper, Shaun
3	Dilcher, Karl
3	Hajir, Farshid
3	Karst, Edgar
3	Kim, Dae San
3	Mendès France, Michel
3	Pollard, John M.
3	Rakaczki, Csaba
3	Rampersad, Narad
3	Roettger, Eric L.
3	Shallit, Jeffrey Outlaw
3	Wen, Zhixiong
3	Williams, Kenneth S.
2	Abdollahi, Farshid
2	Allouche, Jean-Paul Simon
2	Andrews, George Eyre
2	Andrica, Dorin
2	Arias-de-Reyna, Sara
2	Atkin, Arthur Oliver Lonsdale
2	Bagdasar, Ovidiu Dumitru
2	Baillie, Robert
2	Baruah, Nayandeep Deka
2	Berrizbeitia, Pedro
2	Bertolim, Maria Alice
2	Bora, Jonali
2	Chen, Jin
2	Cohen, Graeme L.
2	Compagner, Aaldert
2	Delange, Hubert
2	Dubickas, Artūras
2	Dumas, Jean-Guillaume
2	Dumont, Jean-Marie
2	Fiori, Andrew
2	Forbes, Anthony D.
2	Gao, Shuhong
2	Granville, Andrew James
2	Gugg, Chadwick
2	Hirschhorn, Michael D.
2	Howard, Fredric Timothy
2	Jacquemard, Alain
2	Jordan, James H.
2	Kanasri, Narakorn Rompurk
2	Keith, William J.
2	Knapp, Michael P.
2	Leeming, David J.
2	Lenstra, Arjen K.
2	Lenstra, Hendrik W. jun.
2	Lü, Xiaotao
2	Manasse, Mark S.
2	Mayhew, Gregory L.
2	McDaniel, Wayne L.
2	Mc Laughlin, James G.
2	Mező, István
2	Mullen, Gary L.
2	Novoselov, S. A.
2	Pagi, Gilad
2	Pernet, Clément
2	Pintér, Ákos
2	Pomerance, Carl Bernard
2	Raianu, Şerban
2	Ramaré, Olivier
2	Richstein, Jörg
2	Riesel, Hans
2	Saouter, Yannick
2	Schnorr, Claus Peter
2	Sedoglavic, Alexandre
2	Sell, Elizabeth A.
2	Sills, Andrew V.
2	Silverman, Robert D.
2	Singthongla, Patiwat
2	Southwick, Jeremiah
2	Stoll, Thomas
2	Taghavi, Mohsen
2	te Riele, Herman
2	Thomas, Alain
2	Trotskaia Lehmer, Emma
2	van Rees, G. H. John
2	Vanstone, Scott Alexander
2	Wallisser, Rolf V.
2	Walum, Herbert
2	Wu, Wen
2	Wunderlich, Marvin C.
...and 361 more Authors

all top 5

Cited in 121 Serials

83	Mathematics of Computation
36	Journal of Number Theory
10	The Ramanujan Journal
8	Rocky Mountain Journal of Mathematics
7	Proceedings of the American Mathematical Society
6	Journal of Algebra
6	Journal of Approximation Theory
6	Finite Fields and their Applications
5	Theoretical Computer Science
5	Journal of Integer Sequences
5	BIT. Nordisk Tidskrift for Informationsbehandling
4	Computers & Mathematics with Applications
4	Functiones et Approximatio. Commentarii Mathematici
4	Journal of Computational and Applied Mathematics
4	Transactions of the American Mathematical Society
4	Advances in Applied Mathematics
4	Integers
4	International Journal of Number Theory
3	International Journal of Mathematical Education in Science and Technology
3	Journal of Mathematical Analysis and Applications
3	Annales de l’Institut Fourier
3	Mathematika
3	Monatshefte für Mathematik
3	Journal of Symbolic Computation
3	Journal of Cryptology
3	Bulletin of the American Mathematical Society. New Series
3	Research in Number Theory
2	American Mathematical Monthly
2	Archive for History of Exact Sciences
2	Bulletin of the Australian Mathematical Society
2	Computer Physics Communications
2	Discrete Mathematics
2	Journal of Computational Physics
2	Mathematical Notes
2	Periodica Mathematica Hungarica
2	The Mathematical Intelligencer
2	Acta Arithmetica
2	Advances in Mathematics
2	Annali di Matematica Pura ed Applicata. Serie Quarta
2	Applied Mathematics and Computation
2	BIT
2	Bulletin de la Société Mathématique de France
2	Computing
2	Mathematics and Computers in Simulation
2	Michigan Mathematical Journal
2	Acta Mathematica Hungarica
2	The Journal of Supercomputing
2	Indagationes Mathematicae. New Series
2	Journal de Théorie des Nombres de Bordeaux
2	Journal of Discrete Mathematical Sciences & Cryptography
1	Communications in Algebra
1	Discrete Applied Mathematics
1	Indian Journal of Pure & Applied Mathematics
1	Information Processing Letters
1	Israel Journal of Mathematics
1	Journal d’Analyse Mathématique
1	Linear and Multilinear Algebra
1	Mathematics Magazine
1	Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
1	Compositio Mathematica
1	Czechoslovak Mathematical Journal
1	The Fibonacci Quarterly
1	Fuzzy Sets and Systems
1	International Journal of Mathematics and Mathematical Sciences
1	Journal of Combinatorial Theory. Series A
1	Journal of Pure and Applied Algebra
1	Journal of Soviet Mathematics
1	Kyungpook Mathematical Journal
1	Manuscripta Mathematica
1	Proceedings of the Japan Academy. Series A
1	Proceedings of the London Mathematical Society. Third Series
1	Programming and Computer Software
1	Acta Applicandae Mathematicae
1	Constructive Approximation
1	Information and Computation
1	Japan Journal of Industrial and Applied Mathematics
1	Designs, Codes and Cryptography
1	Aequationes Mathematicae
1	Linear Algebra and its Applications
1	Proceedings of the Indian Academy of Sciences. Mathematical Sciences
1	RAIRO. Informatique Théorique et Applications
1	Applicable Algebra in Engineering, Communication and Computing
1	The Australasian Journal of Combinatorics
1	Vestnik St. Petersburg University. Mathematics
1	Russian Journal of Mathematical Physics
1	Applied and Computational Harmonic Analysis
1	St. Petersburg Mathematical Journal
1	Fractals
1	Filomat
1	Bulletin des Sciences Mathématiques
1	Doklady Mathematics
1	Abstract and Applied Analysis
1	Mathematical Journal of Ibaraki University
1	Annals of Combinatorics
1	Discrete Dynamics in Nature and Society
1	Annals of Mathematics. Second Series
1	Analysis (München)
1	Probability in the Engineering and Informational Sciences
1	Journal of High Energy Physics
1	Comptes Rendus. Mathématique. Académie des Sciences, Paris
...and 21 more Serials

all top 5

Cited in 39 Fields

300	Number theory (11-XX)
37	Computer science (68-XX)
33	Combinatorics (05-XX)
32	Information and communication theory, circuits (94-XX)
26	Algebraic geometry (14-XX)
26	Special functions (33-XX)
23	Field theory and polynomials (12-XX)
22	Numerical analysis (65-XX)
13	Functions of a complex variable (30-XX)
12	Harmonic analysis on Euclidean spaces (42-XX)
7	Group theory and generalizations (20-XX)
7	Dynamical systems and ergodic theory (37-XX)
7	Approximations and expansions (41-XX)
3	History and biography (01-XX)
3	Commutative algebra (13-XX)
3	Real functions (26-XX)
3	Ordinary differential equations (34-XX)
3	Quantum theory (81-XX)
2	Measure and integration (28-XX)
2	Sequences, series, summability (40-XX)
2	Abstract harmonic analysis (43-XX)
2	Integral transforms, operational calculus (44-XX)
2	Geometry (51-XX)
2	Probability theory and stochastic processes (60-XX)
2	Mathematics education (97-XX)
1	Order, lattices, ordered algebraic structures (06-XX)
1	Associative rings and algebras (16-XX)
1	Several complex variables and analytic spaces (32-XX)
1	Partial differential equations (35-XX)
1	Difference and functional equations (39-XX)
1	Functional analysis (46-XX)
1	Operator theory (47-XX)
1	Manifolds and cell complexes (57-XX)
1	Statistics (62-XX)
1	Mechanics of particles and systems (70-XX)
1	Statistical mechanics, structure of matter (82-XX)
1	Relativity and gravitational theory (83-XX)
1	Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1	Biology and other natural sciences (92-XX)

Citations by Year

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