Search: id:A019590
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%I A019590
%S A019590 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A019590 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A019590 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
%N A019590 Fermat's Last Theorem: a(n) = 1 if x^n+y^n=z^n has a nontrivial solution
in integers, otherwise a(n) = 0.
%C A019590 a(n) is the Hankel transform of A000045(n),n>=1 (Fibonacci numbers).
See A055879 for the definition of Hankel transform. W. Lang Jan 23
2007.
%C A019590 1, -1, 0, 0, 0, ... is the convolutional inverse of the all-ones sequence.
- Tanya Khovanova (tanyakh(AT)yahoo.com), Jun 29 2007
%C A019590 a(n) = n - (sum of all natural numbers less than n), if the result is
positive, 0 otherwise. Up to signs and a shift this sequence is the
convolutional inverse of all the one sequence: 1, -1, 0, 0, ... -
Tanya Khovanova (tanyakh(AT)yahoo.com), Jul 14 2007
%D A019590 A. D. Aczel, Fermat's Last Theorem, Four Walls Eight Windows NY 1996
%D A019590 A. C. Clarke, The Last Theorem, Gollancz SF 2004.
%D A019590 B. Cipra, What's Happening in the Mathematical Sciences 1994 Vol. 2,
"A Truly Remarkable Proof" pp. 3-8 AMS Providence RI.
%D A019590 B. Cipra, What's Happening in the Mathematical Sciences 1995-6 Vol. 3,
'Fermat's Theorem-At Last' pp. 2-13 AMS Providence RI.
%D A019590 J. Coates and S.-T. Yau (Eds), Elliptic Curves, Modular Forms and Fermat's
last Theorem, International Press Boston MA 1998.
%D A019590 G. Cornell, J. H. Silverman and G. Stevens (Eds), Modular Forms and Fermat's
last Theorem, Springer NY 2000.
%D A019590 K. J. Devlin, Mathematics:The New Golden Age, Chapter 10, Columbia Univ.
Press NY 1999.
%D A019590 L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public.
256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see
vol. 2, p. 731.
%D A019590 H. M. Edwards, Fermat's Last Theorem, Springer, 1977.
%D A019590 G. Giorello & C. Sinigaglia, "Fermat : De defis en conjectures", Les
genies de la science No.32 Aug-Oct 2007, pp. 82-100, Pour la Science,
Paris.
%D A019590 Y. Hellegouarch, "Fermat Vaincu", Quadrature No. 22 pp. 37-55 Editions
du choix Argenteuil (France) 1995
%D A019590 Y. Hellegouarch, "Fermat enfin demontre", Pour la Science, No. 220, 1996
pp. 92-7 Paris
%D A019590 Y. Hellegouarch, Invitation aux mathematiques de Fermat-Wiles, Dunod
Paris 2001.
%D A019590 Y. Hellegouarch, "L'Enigme du Theoreme de Fermat" pp. 31-41 in 'Qu'est-ce
que l'Univers?", Universite de tous les savoirs, Vol. 4(Edit.Y.Michaud),
Odile Jacob Paris 2001.
%D A019590 Y. Hellegouarch, Invitation to the Mathematics of Fermat-Wiles, Academic
Press NY 2001.
%D A019590 P. Hoffman, The Man Who Loved Only Numbers, pp. 183-200 Hyperion NY 1998
%D A019590 W. Lindsay, Fermat's Last Theorem,A Perfect Proof, Lulu Press,Morrisville
NC 2005.
%D A019590 L. J. Mordell, Three lectures on Fermat's last theorem, Cambr. Univ.
Press 1921 (Reprinted by The scholarly Pub. Office, Univ. of Michigan
Library 2005).
%D A019590 C. J. Mozzochi, The Fermat Diary, AMS Providence RI 2000
%D A019590 C. J. Mozzochi, The Fermat Proof, New Bern NC 2004.
%D A019590 V. K. Murty, Seminar on Fermat's Last Theorem, Amer.Math.Soc. Providence
RI 1995.
%D A019590 P. Odifreddi, The Mathematical Century, Chapter 2.14 " Number Theory
: Wiles' Proof of Fermat's Last Theorem (1995)" pp 82 Princeton Univ.Press
NJ 2004.
%D A019590 I. Peterson, The Mathematical Tourist, pp. 234-8 W.H.Freeman/Owl Book
NY 2001.
%D A019590 I. Peterson, "A Marginal Note" in Islands of Truths, pp. 280-5 W.H.Freeman
NY 1990.
%D A019590 A. van der Poorten, Notes on Fermat's Last Theorem, Wiley NY 1996
%D A019590 J. Propp, Who Proved Fermat's Last Theorem? Princeton Univ. Press NJ
2005.
%D A019590 P. Ribenboim, 13 Lectures on Fermat's Last Theorem, Springer, 1979.
%D A019590 P. Ribenbiom, Fermat's Last Theorem for Amateurs, Springer Verlag NY
1999.
%D A019590 S. Singh, Fermat's Enigma, Walker and Co. NY 1997
%D A019590 I. Stewart, "Fermat's Last Time-Trip", in Scientific American Nov.1993
pp. 85.
%D A019590 I. Stewart, From Here To Infinity, Chapter 3 "Marginal Interest" pp.
25-48 OUP Oxford 1996
%D A019590 I. Stewart and D. Tall, Algebraic Number Theory and Fermat's Last Theorem,
A. K. Peters Natick MA 2001.
%D A019590 G. R. Talbott, Fermat's Last Theorem, Lotus Press WI 1991.
%D A019590 R. Van Vo, Fermat's Last Theorem, AuthorHouse, Bloomington IN 2002.
%D A019590 J. Vigouroux et al., Une aventure mathematique, le theoreme de Fermat,
BT2 series No. 6, PEMF Mouans-Sartoux(France) 1998.
%D A019590 C. Goldstein, "Le Theoreme de Fermat", La Recherche, Vol. 25 March 1994,
pp. 268-275 Paris.
%D A019590 C. Goldstein, "Le Theoreme De Fermat Enfin Demontre", Chapter IX pp.
111-129 in 'Histoire Des Nombres', La Recherche, Tallandier, Paris
2007.
%D A019590 R. Schoof, "Wiles' proof of the Taniyama-Weil conjecture for semi-stable
elliptic curves over Q", Chap. 14 in 'Ou En Sont Les Mathematiques
?' Soc. Math. de France (SMF), Vuibert, Paris 2002.
%H A019590 Amer. Math. Soc.,
Fermat's Last Theorem
%H A019590 Anonymous, Fermat's Last Theorem
%H A019590 A. J. Bailey,
Fermat's Last Theorem
%H A019590 T. Ballard, A Short Form Proof Of
Fermat's Last Theorem
%H A019590 N. Barker, Fermat's
Last Theorem
%H A019590 K. Belabas and C. Goldstein, Fermat et son Theoreme
%H A019590 N. Boston, The Proof
Of Fermat's Last Theorem
%H A019590 K. Buzzard, Review of "Modular Forms and Fermat's
Last Theorem" edited by G. Cornel, J. H. Silverman and G. Stevens
%H A019590 C. K. Caldwell, The Prime Glossary, Fermat's last theorem
%H A019590 A. Camus College Team, La conjecture de Fermat
%H A019590 C. C. Chang, BBC's
Horizon Program: "Fermat's Last Theorem"
%H A019590 C. S. Chinea,
Sobre La Conjetura de Fermat(Text in Italian)
%H A019590 K. Choi, A
Note on Fermat's Last Theorem-Was it a Right Question?
%H A019590 K. Choi, Timeline
of FLT
%H A019590 K. Conrad,
Fermat's Last Theorem For Regular Primes
%H A019590 J. Constant,
Proof of Fermat's Last Theorem
%H A019590 P. Daley, Fermat's
Last Theorem
%H A019590 C. Daney, The
Proof of Fermat's Last Theorem
%H A019590 H. Darmon,
A Proof of the Full Shimura-Taniyama-Weil Conjecture Is Announced
%H A019590 H. Darmon, The Shimura-Taniyama
conjecture (d'apres Wiles)
%H A019590 R. Ellman, A Concise And
Direct Proof of "Fermat's Last Theorem"
%H A019590 K. M. Evans, In Defense of
Mr. Fermat
%H A019590 G. Faltings,
The Proof of Fermat's Last Theorem by R.Taylor and A.Wiles
%H A019590 Larry Freeman's Blog Spot, Fermat's Last Theorem
%H A019590 Daniele A. Gewurz and Francesca Merola, Sequences realized as Parker vectors ..., J. Integer Seqs., Vol. 6, 2003.
%H A019590 C. Gorin,
Fermat's Last Theorem
%H A019590 F. Q. Gouvea, Wiles's Proof, 1993-1995 : Review of "The
Fermat Diary" by C. J. Mozzochi
%H A019590 A. Granville,
Review of BBC's Horizon Program:"Fermat's Last Theorem"
%H A019590 D. Graves, Review of
"Fermat's Last Theorem for Amateurs" by P.Ribenboim
%H A019590 W. F. Hammond, Fermat's Last Theorem after 356 years
%H A019590 W. F. Hammond,
Wiles,Ribet,Shimura-Taniyama-Weil and Fermat's Last Theorem
%H A019590 T. Hausberger, Autour du dernier Theoreme de Fermat
%H A019590 S. Horsler, Home Page on FLT
%H A019590 A. Jackson,
Review of "Fermat's Enigma" by S.Singh
%H A019590 M. Jaiclin,
What Makes Fermat's Last Theorem So Hard, Anyway?
%H A019590 N. de Jong, Fermat's
Last Theorem. Was Wiles's proof really first?
%H A019590 D. Kaminski,
The extraordinary story of Fermat's Last Theorem
%H A019590 A. Krowne, PlanetMath.org, Fermat's last theorem
%H A019590 S. Lang, Some History
of the Shimura-Taniyama Conjecture
%H A019590 W. Lang,
On generalizations of Stirling number triangles, J. Integer Seqs.,
Vol. 3 (2000), #00.2.4.
%H A019590 L. Lemaire,
Le theoreme de Fermat-Wiles (pages 5-11/35)
%H A019590 R. Lisker,
Fermat's Last Theorem (Conference Report)
%H A019590 A. Lopez-Ortiz, What We Know
About Fermat's Last Theorem
%H A019590 E. R. Lucier, Fermat's Last
Theorem,Further Study
%H A019590 L. Lusk,
A Brief History of Fermat's Last Theorem
%H A019590 M. Marcionelli,
La conjecture de Fermat
%H A019590 Mathematical Database, Poster, Fermat's Last Theorem
%H A019590 Mathforum,
Fermat's Last Theorem
%H A019590 G. Mazzarino, Fermat's Last Theorem
%H A019590 G. Mazzarino, Fermat's Last Theorem Revisited
%H A019590 P. L. Mills,
Fermat's Last Theorem-A New Proof
%H A019590 J. S. Milne,
Elliptic Curves
%H A019590 New York Times,
"Fermat's Enigma" by S. Singh; Chapter 1
%H A019590 J. J. O'Connor and E. F. Robertson, Fermat's Last Theorem
%H A019590 R. Osserman et al., Fermat's Last Theorem : A Supplement
to the Video
%H A019590 I. Peterson,
Curving Beyond Fermat
%H A019590 A. van der Poorten,
"Notes on Fermat's Last Theorem": Table of Contents
%H A019590 A. van der Poorten, Fermat's Last Theorem
%H A019590 J. Propp,
Bibliography of articles on FLT
%H A019590 S. Rees, Fermat's
Last Theorem
%H A019590 D. Rideout,
Pythagorean Triples, the Unit Circle and Fermat's Last Theorem
%H A019590 K. Rubin,
The Solving of Fermat's Last Theorem (Slides)
%H A019590 K. Rubin and A. Silverberg, A Report on Wiles' Cambridge Lectures
%H A019590 K. Rubin and A. Silverberg,
A report on Wiles' Cambridge lectures
%H A019590 K. Rubin and A. Silverberg, A Report On Wiles' Cambridge Lectures
%H A019590 D. Rusin, The Mathematical Atlas, Higher degree equations; Fermat's equation
%H A019590 School of Mathematics and Statistics, University of St Andrews,
Fermat's last theorem.
%H A019590 P. Schorer, Is There a
"Simple" Proof of Fermat's Last Theorem
%H A019590 J. L. Selfridge, C. A. Nicol and H. S. Vandiver, Proof Of Fermat's Last Theorem For All
Prime Exponents Less Than 4002
%H A019590 D. Shay, Fermat's Last Theorem
%H A019590 Kaida Shi,
The n-dimensional Cube--A New Way to Prove the Fermat's Last Theorem
%H A019590 S. Singh, Fermat
Corner
%H A019590 S. Singh,
Fermat's Last Theorem
%H A019590 S. Somani, The Saga of Fermat's Last Theorem
%H A019590 K. Spiliopoulos,
The Final Milestones in the Proof of Fermat's Last Theorem
%H A019590 S. Stedman,
Fermat's Last Theorem
%H A019590 W. A. Stein, Fermat's Last Theorem and Modularity
of Elliptic Curves
%H A019590 D. Surendran,
Fermat's Last Theorem
%H A019590 Think Quest,
The final stages in proving Fermats Last Theorem
%H A019590 C. Thornhill,
Fermat's Last Theorem
%H A019590 D. L. Vestal, Review
of "Invitation to the Mathematics of Fermat-Wiles" by Y. Hellegouarch
%H A019590 G. Villemin's Almanach of Numbers, Theoreme de Fermat-Wiles
%H A019590 A. H. Warren, Proof Of The Fermat's Last Theorem
%H A019590 Wikipedia,
Fermat's Last Theorem
%H A019590 A. J. Wiles, Modular elliptic curves and Fermat's last
theorem, Ann. Math. 141 (1995), 443-551.
%H A019590 A. J. Wiles,
Modular elliptic curves and Fermat's Last Theorem
%H A019590 T. Yee, The Fermat's Last
Theorem(FLT)
%H A019590 YouTube,
BBC's Horizon Program : "Fermat's Last Theorem" in 5 parts
%F A019590 a(n)=(-1)^n*sum{k=0..floor(n/2), (-1)^A010060(n-2k)mod(C(n, 2k), 2)}
- Paul Barry (pbarry(AT)wit.ie), Jan 03 2005
%F A019590 a(n)=1-[(n+2) mod (n+1)]+[n!^2 mod (n+1)]*[(n+1)!^2 mod (n+2)]; - Paolo
P. Lava (ppl(AT)spl.at), Aug 29 2007
%F A019590 a(n)=[(n-1)! mod 2], with n>=1 - Paolo P. Lava (ppl(AT)spl.at), Feb 15
2008
%F A019590 a(n+1)=(1/2)*[1+(-1)^n]*a(n), with a(0)=1 - Paolo P. Lava (ppl(AT)spl.at),
Apr 16 2008
%F A019590 Euler transform of length 2 sequence [ 1, -1]. - Michael Somos Jul 05
2009
%F A019590 a(n) is multiplicative with a(2) = 1, a(2^e) = 0 if e>1, a(p^e) = 0^e
if p>2. - Michael Somos Jul 05 2009
%F A019590 G.f.: x + x^2 = x * (1 - x^2) / (1 - x). - Michael Somos Jul 05 2009
%F A019590 Dirichlet g.f.: 1 + 2^(-s). - Michael Somos Jul 05 2009
%o A019590 (PARI) {a(n) = (n==1) + (n==2)} /* Michael Somos Jul 05 2009 */
%Y A019590 Cf. A000004, A000007, A010051, A012450.
%Y A019590 INVERT transform gives Fibonacci numbers, A000045.
%Y A019590 Convolution inverse of A062157. Dirichlet convolution inverse of A154269.
%Y A019590 Sequence in context: A105812 A134323 A060576 this_sequence A154955 A014040
A014071
%Y A019590 Adjacent sequences: A019587 A019588 A019589 this_sequence A019591 A019592
A019593
%K A019590 nonn,nice,easy,mult
%O A019590 1,1
%A A019590 N. J. A. Sloane (njas(AT)research.att.com).
%E A019590 Additional links provided by Lekraj Beedassy (blekraj(AT)yahoo.com),
Nov 20 2003
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