Sur la fonction plus grand facteur premier

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1. [1] Baker ( A.). - Transcendental number theory. - Cambridge, Cambridge University Press, 1975. Zbl0297.10013MR422171
2. [2] Birkhoff ( G.D.) and Vandiver ( H.S.). - On the integral divisors of an-bn , Annals of Math., Series 2, t. 5, 1904, p. 173-180. MR1503541JFM35.0205.01
3. [3] Cassels ( J.W.S.). - An introduction to diophantine approximation. 2nd edition. - Cambridge, Cambridge University Press, 1965. MR87708
4. [4] Cassels ( J.W.S.). - On a class of exponential equations, Arkiv. für Math., t. 4, 1963, p. 231-233. Zbl0102.03507MR130217
5. [5] Catalan ( E.). - Note extraite d'une lettre adressée à l'éditeur, J. reine angew. Math., t. 27, 1844, p. 192. 
6. [6] Chowla ( S.). - The greastest prime factor of x2 + 1 , J. London math. Soc., t. 10, 1935, p. 117-120. Zbl0011.29305
7. [7] Cramer ( H.). - On the order of magnitude of the difference between consecutive prime numbers, Acta Arithm., Warszawa, t. 2, 1937, p. 23-46. JFM62.1147.01
8. [8] Deshouillers ( J.M.). - Le théorème de Sylvester et Schur (dactylographié). 
9. [9] Erdös ( P.). - A theorem of Sylvester and Schur, J. London math. Soc., t. 9, 1934, p. 282-288. Zbl0010.10302
10. [10] Erdös ( P.). - On consecutive integers, Nieuw Arch. voor Wisk., t. 3, 1955, p. 124-128. Zbl0065.27605MR73628
11. [11] Erdös ( P.). - On the normal number of prime factors of p - 1 and some related problems concerning Euler Ø-function, Quaterly J. of Math., t. 6, 1935, p. 203-213. Zbl0012.14905JFM61.0129.05
12. [12] Erdös ( P.). - On the greatest prime factor of Πxk=1 f(k) , J. London math. Soc., t. 27, 1952, p. 379-384. Zbl0046.04102
13. [13] Erdös ( P.). - Some problems in number theory, "Computers in number theory", Proceedings of a symposium held at Oxford, 1969, p. 405-414. - London, New York, Academic Press, 1971. Zbl0217.03101
14. [14] Erdös ( P.) and Selfridge ( J.L.). - Some problems on the prime factors of consecutive integers, II, "Proceedings Washington State University Conference of number theory, Pullman1971" (à paraître). Zbl0228.10028MR318076
15. [15] Erdös ( P.) and Shorey ( T.N.). - On the greastest prime factor of 2P - 1 for a prime p and other expressions, Acta Arithm., Warszawa (à paraître). Zbl0296.10021
16. [16] Fel'dman ( N.I.). - Improved estimate for a linear form of the logarithms of algebraic numbers, Math. of the USSR-Sbornik, t. 6, 1968, p. 393-406 ; [en russe] Mat. Sbornik, N. S., t. 77, 1968, p. 423-436. Zbl0235.10018
17. [17] Gel'fond ( A.O.). - Transcendental and algebraic numbers. - New York, Dover Publications, 1960. Zbl0090.26103MR111736
18. [18] Halberstam ( H.). - On the distribution of additive number theoretic function, II and III., J. London math. Soc., t. 31, 1956, p. 1-11, 14-31. Zbl0071.04203MR73626
19. [19] Halberstam ( H.). - Numbers with a large prime factors, Séminaire de Théorie des nombres de l'Université de Bordeaux, 1971/72, exp. 23. Zbl0274.10041
20. [20] Hall ( Marshall Jr.). - The diophantine equation x3 - y2 = k , "Computers in number theory", Proceedings of a symposium held at Oxford, 1969, p. 173-198. - London, New York, Academic Press, 1971. Zbl0225.10012MR323705
21. [21] Hanson ( D.). - On the product of the primes, Canad. math. Bull., t. 15, 1972, p. 33-37. Zbl0231.10008MR313179
22. [22] Hardy ( G.H.) and Wright ( E.M.). - An introduction to the theory of numbers, 4th edition. - Oxford, Clarendon Press, 1959. Zbl0086.25803MR67125
23. [23] Huxley ( M.N.). - On the difference between consecutive primes, Inventiones Math., Berlin, t. 15, 1972, p. 164-170. Zbl0241.10026MR292774
24. [24] Jutila ( M.). - On numbers with a large prime factor, Indian J. of Math. (à paraître). Zbl0293.10023
25. [25] Kotov ( S.V.). - The greatest prime factor of a polynomial, Math. Notes, t. 13, 1973, p. 313-317 ; [en russe], Mat. Zametki, t. 13, 1973, p. 515-522. Zbl0267.12002MR327670
26. [26] Landau ( E.). - Primzahlen. - New York, Chelsea publishing Company, 1953. MR68565
27. [27] Langevin ( M.). - Plus grand facteur premier d'entiers consécutifs, C. R. Acad. Sc. Paris, t. 280, 1975, Série A, p. 1567-1570. Zbl0305.10041MR379403
28. [28] Langevin ( M.). - Plus grand facteur premier d'entiers voisins, C. R. Acad. Sc. Paris (à paraître). Zbl0311.10044
29. [29] Lehmer ( D.H.). - On a problem of Störmer, Illinois J. Math., t. 8, 1964, p. 57-79. Zbl0124.27202MR158849
30. [30] Mahler ( K.). - Zur approximation algebraischer Zahlen, I und II., Math. Annalen, t. 107, 1933, p. 691-730, t. 108,1933, p. 37-55. Zbl0006.10502MR1512822
31. [31] Mahler ( K.). - Über den grössten Primteiler der Polynome x2 ∓ 1 , Archiv for Math. og Naturvid, t. 41, 1935, n° 1, 8 p. Zbl0012.39405
32. [32] Mahler ( K.). - Über den grössten Primteiler spezieller Polynome zweiten Grades, Arch. for Math. og Naturvid., t. 41, 1935, n° 6, 26 p. Zbl0013.38903
33. [33] Mahler ( K.). - On the greatest prime factor of axm + byn , Nieuw Archief voor Wiskunde, 3e série, t. 1, 1953, p. 113-122. Zbl0050.26804MR57899
34. [34] Mordell ( L.J.). - Diophantine Equations. - London, New York, Academic Press, 1969 (Pure and applied Mathematics, Academic Press, 30). Zbl0188.34503MR249355
35. [35] Nagell ( T.). - Über den grössten Primteiler gewisser Polynome dritten Grades, Math. Annalen, t. 114, 1937, p. 284-292. Zbl0016.10104MR1513139
36. [36] Perron ( O.). - Die Lehre von den Kettenbruchen, 3te Auflage. Band 1. - Stuttgart, B. G. Teubner, 1954. Zbl0056.05901MR64172
37. [37] Polya ( G.). - Zur arithmetischen Untersuchung der Polynome, Math. Z., t. 1, 1918, p. 143-148. MR1544288JFM46.0240.04
38. [38] Prachar ( K.). - Primzahlverteilung. - Berlin, Springer-Verlag, 1957 (Grundlehren der mathematischen Wissenschaften, 91). Zbl0080.25901MR87685
39. [39] Ramachandra ( K.). -Largest prime factor of the product of k-consecutive integers, "Proceedings of the international conference on number theory, Moscou, 1971" (à paraître). MR337831
40. [40] Ramachandra ( K.). - A note on numbers with a large prime factor, III., Acta Arithm., Warszawa, t. 19, 1971, p. 49-62. Zbl0218.10058MR299569
41. [41] Ramachandra ( K.). - Application of Baker's theory to two problems considered by Erdös and Selfridge, J. Indian math. Soc., t. 37, 1973, p. 25-34. Zbl0326.10038MR364121
42. [42] Ramachandra ( K.). and Shorey ( T.N.). - On gaps between numbers with a large prime factor, Acta Arithm., Warszawa, t. 24, 1973, p. 99-111. Zbl0258.10022MR327684
43. [43] Rankin ( R.A.). - The difference between consecutive prime numbers, J. London math. Soc., t. 13, 1938, p. 232-247 ; et Proc. Edinburgh math. Soc., t. 13, 1963, p. 331-332. Zbl0019.39403MR160767JFM64.0982.01
44. [44] Schinzel ( A.). - On two theorems of Gel'fond and some of their applications, Acta Arithm., Warszawa, t. 13, 1967, p. 177-236. Zbl0159.07101MR222034
45. [45] Schinzel ( A.). - On primitive prime factors of an - bn , Proc. Cambridge phil. Soc., t. 58, 1962, p. 555-562. Zbl0114.02605MR143728
46. [46] Schmidt ( W.). - Approximation to algebraic numbers. - Genève, l'Enseignement mathématique, 1972 (Monographies de l'Enseignement mathématique, 19). MR344203
47. [47] Schönhage ( A.). - Eine Bemerkung zur Konstruktion grosser Primzahllücken, Arch. der Math., t. 14, 1963, p. 29-30. Zbl0108.04504MR146154
48. [48] Schur ( J.). - Einige Sätze über Primzahlen mit Anwendung auf Irreduzibilitätsfragen, Sitz. der Preuss. Akad. Wiss., Phys. Math. Klasse, t. 23, 1929, p. 1-24. JFM55.0069.03
49. [49] Shorey ( T.N.). - On gaps between numbers with a large prime factor, II., Acta Arithm., Warszawa, t. 25, 1974, p. 365-373. Zbl0258.10023MR344201
50. [50] Shorey ( T.N.). - On linear forms in the logarithms of algebraic numbers, Acta Arithm., Warszawa (à paraître). Zbl0289.10023
51. [51] Shorey ( T.N.) and Tijdeman ( R.). - On the greatest prime factor of polynomials at integer points, Acta Arithm., Warszawa (à paraître). 
52. [52] Siegel ( C.L.). - Approximation algebraischen Zahlen, Math. Z., t. 10, 1921, p. 173-213. MR1544471JFM48.0163.07
53. [53] Siegel ( C.L.). - The integer solutions of the equation y2=axn+bxn-1+...+k , (extrait d'une lettre à L. J. Mordell), J. London math. Soc., t. 1, 1926, p. 66-68. 
54. [54] Sprindžuk ( V.G.). - An improvement of the estimate of rational approximations to algebraic numbers, Dokl. Akad. Nauk Belorusskoj SSR, t. 15, 1971, p. 101-104. MR292763
55. [55] Sprindžuk ( V.G.). - Diviseurs sans facteurs carrés des polynômes et nombre de classes des corps de nombres algébriques [en russe], Acta Arithm., Warszawa, t. 24, 1973, p. 143-149. 
56. [56] Stark ( H.M.). - Effective estimates of solutions of some diophantine equations, Acta Arithm., Warszawa, t. 24, 1973, p. 251-259. Zbl0272.10010MR340175
57. [57] Stewart ( C.L.). - The greatest prime factor of an - bn , Acta Arithm., Warszawa, (à paraître). Zbl0313.10007
58. [58] Størmer ( C.). - Quelques théorèmes sur l'équation de Pell x2-Dy2=±1 et leurs applications, Christiana Videnskabsselskabs Skrifter, Mat. Naturv. Kl., 1897, n° 2, 48 p. JFM28.0192.02
59. [59] Sylvester ( J.J.). - On arithmetical series, Messenger of Math., t. 21, 1892, p. 1-19, 87-120. JFM23.0181.02
60. [60] Tijdeman ( R.). - Old and new in number theory, Nieuw Arch. voor Wiskunde, 3e série, t. 20, 1972, p. 20-30. Zbl0227.10001MR300983
61. [61] Tijdeman ( R.). - On integers with many small prime factors, Comp. Math., Groningen, t. 26, 1973, p. 319-330. Zbl0267.10056MR325549
62. [62] Tijdeman ( R.). - On the maximal distance between integers composed of small primes, Comp. Math., Groningen, t. 28, 1974, p. 159-162. Zbl0283.10024MR345917
63. [63] Tijdeman ( R.) and Meijer ( H.G.). - On integers generated by a finite number of fixed primes, Comp. Math., Groningen, t. 29, 1974, p. 273-286. Zbl0297.10030MR364122
64. [64] Tijdeman ( R.). - On the equation of Catalan, Acta Arithm., Warszawa (à paraître). Zbl0286.10013
65. [65] Tuckerman ( B.). - The 24th Mersenne prime, Notices Amer. math. Soc., t. 18, 1971, p. 608. Zbl0224.10006MR291072
66. [66] Poorten ( A. van der). - A p-adic analogue of an inequality of Baker for linear forms in the logarithms of algebraic numbers, Austral. J. of Math (à paraître). 
67. [67] Waldschmidt ( M.). - Minorations effectives de formes linéaires de logarithmes, Séminaire Delange-Pisot-Poitou : Groupe d'étude de théorie des nombres, 15e année, 1973/74, n° G3, 8 p. Zbl0324.10028
68. [68] Zsigmondy ( K.). - Zur Theorie der Potenzreste, Monatsh. Math., t. 3, 1892, p. 265-284. JFM24.0176.02

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