Some applications of linear forms in logarithms

 Access to full text

 Full (PDF)

1. [1] Baker ( A.). - Linear forms in the logarithms of algebraic numbers, I, Mathematika, London, t. 13, 1966, p. 204-216. Zbl0161.05201MR258756
2. [2] Baker ( A.). - Linear forms in the logarithms of algebraic numbers, IV, Mathematika, London, t. 15, 1968, p. 204-216. Zbl0169.37802MR258756
3. [3] 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
4. [4] Coates ( J.). - An effective p-adic analogue of a theorem of Thue, Acta Arithm., Warszawa, t. 15, 1969, p. 279-305. Zbl0221.10025MR242768
5. [5] Erdös ( P.). - On the greatest prime factor of Πxk=1 f(k) , J. London math. Soc., t. 27, 1952, p. 379-384. Zbl0046.04102
6. [6] Erdös ( P.). - Some recent advances and current problems in number theory, "Lectures on modern mathematics", Vol. III, p. 196-244. - New York, J. Wiley and Sons, 1965. Zbl0132.28402MR177933
7. [7] Erdös ( P.) and Selfridge ( J.L.). - Some problems on the prime factors of consecutive integers, Illinois J. Math., t. 11, 1967, p. 428-430. Zbl0149.28901MR229570
8. [8] Erdös ( P.) and Selfridge ( J.L.). - Some problems on the prime factors of consecutive integers, II., "Proceedings of the Washington State University conference on number theory", p. 13-21. - Pullman, Washington State University, 1971. Zbl0228.10028MR318076
9. [9] Erdös ( P.) and Shorey ( T.N.). - On the greatest prime factor of 2p - 1 for a prime p and other expressions, Acta Arithm., t. 30, 1976, p. 257-265. Zbl0296.10021MR419381
10. [10] Grimm ( C.A.). - A conjecture on consecutive composite numbers, Amer. math. Monthly, t. 76, 1969, p. 1126-1128. Zbl0197.32001MR260668
11. [11] Jutila ( M.). - On numbers with a large prime factor, II., J. Indian math. Soc., t. 38, 1974, p. 125-130. Zbl0335.10045MR399013
12. [12] Keates ( M.). - On the greatest prime factor of a polynomial, Proc. Edinburgh math. Soc., Series 2, t. 16, 1969, p. 301-308. Zbl0188.10201MR257034
13. [13] Kotov ( S.V.). - Greatest prime factor of a polynomial, Math. Notes, t. 13, 1973, p. 313-317 ; and [in Russian] Mat. Zametki, t. 13, 1973, p. 515-522. Zbl0267.12002MR327670
14. [14] Langevin ( M.). - Plus grand facteur premier d'entiers consécutifs, C. R. Acad. Sc. Paris, t. 280, 1975, Serie A, p. 1567-1570. Zbl0305.10041MR379403
15. [15] Langevin ( M.). - Plus grand facteur premier d'entiers voisins, C. R. Acad. Sc. Paris, t. 281, 1975, Série A, p. 491-493. Zbl0311.10044MR396442
16. [16] Mahler ( K.). - Ein Analogon zu einem Schneiderschen Satz, Koninkl. Nederl. Akad. Wetensch., Proc., t. 39, 1936, p. 633-640 and p. 729-737. Zbl0014.20502JFM62.0186.01
17. [17] Ramachandra ( K.). - Application of Baker's theory to two problems consired by Erdös and Selfridge, J. Indian math. Soc., t. 37, 1973, p. 25-34. Zbl0326.10038MR364121
18. [18] 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
19. [19] Ramachandra ( K.), Shorey ( T.N.) and Tijdeman ( R.). - On Grimm's problem relating to factorisation of a block of consecutive integers, II., J. reine angew. Math. (to appear). Zbl0333.10028
20. [20] Ridout ( D.). - Rational approximations to algebraic numbers, Mathematika, London, t. 4, 1957, p. 125-131. Zbl0079.27401MR93508
21. [21] Schinzel ( A.). - On primitive prime factors of an - bn , Proc. Cambridge philos. Soc., t. 58, 1962, p. 555-562. Zbl0114.02605MR143728
22. [22] Schinzel ( A.). - On two theorems of Gel'fond and some of their applications, Acta Arithm., Warszawa, t. 13, 1967, p. 177-236. Zbl0159.07101MR222034
23. [23] Shorey ( T.N.). - On gaps between numbers with a large prime factor, II., Acta Arithm., Warszawa, t. 25, 1974, p. 365 - 373. Zbl0258.10023MR344201
24. [24] Shorey ( T.N.). - On linear forms in the logarithms of algebraic numbers, Acta Arithm., Warszawa, t. 30, 1976, p. 37-42. Zbl0289.10023MR412117
25. [25] Shorey ( T.N.) and Tijdeman ( R.). - On the greatest prime factor of polynomials at integer points (to appear). Zbl0338.10040MR424681
26. [26] Siegel ( C.L.). - Approximation algebraischer Zahlen, Math. Z., t. 10, 1921, p. 173-213. MR1544471JFM48.0163.07
27. [27] Sprindžuk ( V.G.). - The greatest prime factor of a binary form, Dokl. Akad. Nauk BSSR, t. 15, 1971, p. 389-391. MR286752
28. [28] Stewart ( C.L.). - The greatest prime factor of an - bn , Acta Arithm., Warszawa, t. 26, 1975, p. 427-433. Zbl0313.10007MR398993
29. [29] Tijdeman ( R.). - On integers with many small prime factors, Compositio Math., Groningen, t. 26, 1973, p. 319-330. Zbl0267.10056MR325549
30. [30] Zsigmondy ( K.). - Zur Theorie der Potenzreste, Monatsh. fUr Math., t. 3, 1892, p. 265-289. JFM24.0176.02