Sur la fonction plus grand facteur premier
Séminaire Delange-Pisot-Poitou. Théorie des nombres, Volume 16 (1974-1975) no. 2, Talk no. G22, 29 p.
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Langevin, Michel. Sur la fonction plus grand facteur premier. Séminaire Delange-Pisot-Poitou. Théorie des nombres, Volume 16 (1974-1975) no. 2, Talk no. G22, 29 p. http://www.numdam.org/item/SDPP_1974-1975__16_2_A18_0/

[1] Baker (A.). - Transcendental number theory. - Cambridge, Cambridge University Press, 1975. | MR | Zbl

[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. | JFM | MR

[3] Cassels (J.W.S.). - An introduction to diophantine approximation. 2nd edition. - Cambridge, Cambridge University Press, 1965. | MR

[4] Cassels (J.W.S.). - On a class of exponential equations, Arkiv. für Math., t. 4, 1963, p. 231-233. | MR | Zbl

[5] Catalan (E.). - Note extraite d'une lettre adressée à l'éditeur, J. reine angew. Math., t. 27, 1844, p. 192. | Zbl

[6] Chowla (S.). - The greastest prime factor of x2 + 1 , J. London math. Soc., t. 10, 1935, p. 117-120. | Zbl

[7] Cramer (H.). - On the order of magnitude of the difference between consecutive prime numbers, Acta Arithm., Warszawa, t. 2, 1937, p. 23-46. | JFM

[8] Deshouillers (J.M.). - Le théorème de Sylvester et Schur (dactylographié).

[9] Erdös (P.). - A theorem of Sylvester and Schur, J. London math. Soc., t. 9, 1934, p. 282-288. | Zbl

[10] Erdös (P.). - On consecutive integers, Nieuw Arch. voor Wisk., t. 3, 1955, p. 124-128. | MR | Zbl

[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. | JFM | Zbl

[12] Erdös (P.). - On the greatest prime factor of Πxk=1 f(k) , J. London math. Soc., t. 27, 1952, p. 379-384. | Zbl

[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. | Zbl

[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, Pullman 1971" (à paraître). | MR | Zbl

[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). | Zbl

[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. | Zbl

[17] Gel'Fond (A.O.). - Transcendental and algebraic numbers. - New York, Dover Publications, 1960. | MR | Zbl

[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. | MR | Zbl

[19] Halberstam (H.). - Numbers with a large prime factors, Séminaire de Théorie des nombres de l'Université de Bordeaux, 1971/72, exp. 23. | Zbl

[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. | MR | Zbl

[21] Hanson (D.). - On the product of the primes, Canad. math. Bull., t. 15, 1972, p. 33-37. | MR | Zbl

[22] Hardy (G.H.) and Wright (E.M.). - An introduction to the theory of numbers, 4th edition. - Oxford, Clarendon Press, 1959. | MR | Zbl

[23] Huxley (M.N.). - On the difference between consecutive primes, Inventiones Math., Berlin, t. 15, 1972, p. 164-170. | MR | Zbl

[24] Jutila (M.). - On numbers with a large prime factor, Indian J. of Math. (à paraître). | Zbl

[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. | MR | Zbl

[26] Landau (E.). - Primzahlen. - New York, Chelsea publishing Company, 1953. | MR

[27] Langevin (M.). - Plus grand facteur premier d'entiers consécutifs, C. R. Acad. Sc. Paris, t. 280, 1975, Série A, p. 1567-1570. | MR | Zbl

[28] Langevin (M.). - Plus grand facteur premier d'entiers voisins, C. R. Acad. Sc. Paris (à paraître). | Zbl

[29] Lehmer (D.H.). - On a problem of Störmer, Illinois J. Math., t. 8, 1964, p. 57-79. | MR | Zbl

[30] Mahler (K.). - Zur approximation algebraischer Zahlen, I und II., Math. Annalen, t. 107, 1933, p. 691-730, t. 108,1933, p. 37-55. | MR | Zbl

[31] Mahler (K.). - Über den grössten Primteiler der Polynome x2 ∓ 1 , Archiv for Math. og Naturvid, t. 41, 1935, n° 1, 8 p. | Zbl

[32] Mahler (K.). - Über den grössten Primteiler spezieller Polynome zweiten Grades, Arch. for Math. og Naturvid., t. 41, 1935, n° 6, 26 p. | Zbl

[33] Mahler (K.). - On the greatest prime factor of axm + byn , Nieuw Archief voor Wiskunde, 3e série, t. 1, 1953, p. 113-122. | MR | Zbl

[34] Mordell (L.J.). - Diophantine Equations. - London, New York, Academic Press, 1969 (Pure and applied Mathematics, Academic Press, 30). | MR | Zbl

[35] Nagell (T.). - Über den grössten Primteiler gewisser Polynome dritten Grades, Math. Annalen, t. 114, 1937, p. 284-292. | MR | Zbl

[36] Perron (O.). - Die Lehre von den Kettenbruchen, 3te Auflage. Band 1. - Stuttgart, B. G. Teubner, 1954. | MR | Zbl

[37] Polya (G.). - Zur arithmetischen Untersuchung der Polynome, Math. Z., t. 1, 1918, p. 143-148. | JFM | MR

[38] Prachar (K.). - Primzahlverteilung. - Berlin, Springer-Verlag, 1957 (Grundlehren der mathematischen Wissenschaften, 91). | MR | Zbl

[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). | MR

[40] Ramachandra (K.). - A note on numbers with a large prime factor, III., Acta Arithm., Warszawa, t. 19, 1971, p. 49-62. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | JFM | MR | Zbl

[44] Schinzel (A.). - On two theorems of Gel'fond and some of their applications, Acta Arithm., Warszawa, t. 13, 1967, p. 177-236. | MR | Zbl

[45] Schinzel (A.). - On primitive prime factors of an - bn , Proc. Cambridge phil. Soc., t. 58, 1962, p. 555-562. | MR | Zbl

[46] Schmidt (W.). - Approximation to algebraic numbers. - Genève, l'Enseignement mathématique, 1972 (Monographies de l'Enseignement mathématique, 19). | MR

[47] Schönhage (A.). - Eine Bemerkung zur Konstruktion grosser Primzahllücken, Arch. der Math., t. 14, 1963, p. 29-30. | MR | Zbl

[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. | JFM

[49] Shorey (T.N.). - On gaps between numbers with a large prime factor, II., Acta Arithm., Warszawa, t. 25, 1974, p. 365-373. | MR | Zbl

[50] Shorey (T.N.). - On linear forms in the logarithms of algebraic numbers, Acta Arithm., Warszawa (à paraître). | Zbl

[51] Shorey (T.N.) and Tijdeman (R.). - On the greatest prime factor of polynomials at integer points, Acta Arithm., Warszawa (à paraître).

[52] Siegel (C.L.). - Approximation algebraischen Zahlen, Math. Z., t. 10, 1921, p. 173-213. | JFM | MR

[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] 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. | MR

[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] Stark (H.M.). - Effective estimates of solutions of some diophantine equations, Acta Arithm., Warszawa, t. 24, 1973, p. 251-259. | MR | Zbl

[57] Stewart (C.L.). - The greatest prime factor of an - bn , Acta Arithm., Warszawa, (à paraître). | Zbl

[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. | JFM

[59] Sylvester (J.J.). - On arithmetical series, Messenger of Math., t. 21, 1892, p. 1-19, 87-120. | JFM

[60] Tijdeman (R.). - Old and new in number theory, Nieuw Arch. voor Wiskunde, 3e série, t. 20, 1972, p. 20-30. | MR | Zbl

[61] Tijdeman (R.). - On integers with many small prime factors, Comp. Math., Groningen, t. 26, 1973, p. 319-330. | Numdam | MR | Zbl

[62] Tijdeman (R.). - On the maximal distance between integers composed of small primes, Comp. Math., Groningen, t. 28, 1974, p. 159-162. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[64] Tijdeman (R.). - On the equation of Catalan, Acta Arithm., Warszawa (à paraître). | Zbl

[65] Tuckerman (B.). - The 24th Mersenne prime, Notices Amer. math. Soc., t. 18, 1971, p. 608. | MR | Zbl

[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] 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. | Numdam | Zbl

[68] Zsigmondy (K.). - Zur Theorie der Potenzreste, Monatsh. Math., t. 3, 1892, p. 265-284. | JFM