@article{CM_1988__66_1_37_0, author = {Erd\"os, P\'al and Stewart, Cameron L. and Tijdeman, Robert}, title = {Some diophantine equations with many solutions}, journal = {Compositio Mathematica}, volume = {68}, year = {1988}, pages = {37-56}, mrnumber = {937987}, zbl = {0639.10014}, language = {en}, url = {http://dml.mathdoc.fr/item/CM_1988__66_1_37_0} }
Erdös, P.; Steward, C. L.; Tijdeman, R. Some diophantine equations with many solutions. Compositio Mathematica, Tome 68 (1988) pp. 37-56. http://gdmltest.u-ga.fr/item/CM_1988__66_1_37_0/
1 Contributions to the theory of Diophantine equations. I. On the representation of integers by binary forms, Philos. Trans. Roy. Soc. London Ser. A 263 (1967/68) 173-191. | MR 228424 | Zbl 0157.09702
,2 On sums of sequences of integers, II, Acta Math. Hungar. 44 (1984) 169-179. | MR 759044 | Zbl 0559.10034
and ,3 On Thue's equation, Invent. Math. 88 (1987) 69-81. | MR 877007 | Zbl 0614.10018
and ,4 The asymptotic behaviour of a function occurring in the theory of primes, J. Indian Math. Soc. (N.S.) 15 (1951) 25-32. | MR 43838 | Zbl 0043.06502
,5 On the number of positive integers ≤ x and free of prime factors > y, Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951) 50-60. | Zbl 0042.04204
,6 On those numbers in an arithmetical progression all prime factors of which are small in order of magnitude (Russian), Dokl. Akad. Nauk. SSSR 67 (1949) 5-8. | MR 30995
,7 On a problem of Oppenheim concerning 'Factorisatio Numerorum', J. Number Th. 17 (1983) 1-28. | MR 712964 | Zbl 0513.10043
, and ,8 A probabilistic approach to a differential-difference equation arising in analytic number theory, Math. Comp. 27 (1973) 197-203. | MR 336952 | Zbl 0252.65066
,9 An effective p-adic analogue of a theorem of Thue, Acta Arith. 15 (1968/69) 279-305. | MR 242768 | Zbl 0221.10025
,10 An effective p-adic analogue of a theorem of Thue II, The greatest prime factor of a binary form, Acta Arith. 16 (1969/70) 399-412. | MR 263741 | Zbl 0221.10026
,11 Rational approximations to algebraic numbers, Mathematika 2 (1955) 160-167. | MR 77577 | Zbl 0066.29302
and ,12 On the frequency of numbers containing prime factors of a certain relative magnitude, Ark. Mat. Astr. Fys. 22 (1930) A10, 1-14. | JFM 56.0178.04
,13 The difference of consecutive primes, Duke Math. J. 6 (1940) 438-441. | JFM 66.0162.04 | MR 1759 | Zbl 0023.29801
,14 Problems in number theory and combinatorics, Proc. 6th Manitoba Conference on Numerical Mathematics, Congress Numer. 18, Utilitas Math., Winnipeg, Man. (1977) 35-58. | MR 532690 | Zbl 0471.10002
,15 On a problem in the elementary theory of numbers, Amer. Math. Monthly 41 (1934) 608-611. | JFM 60.0917.05 | MR 1523239 | Zbl 0010.29401
and ,16 On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984) 561-584. | MR 735341 | Zbl 0521.10015
,17 On unit equations and decomposable form equations, J. reine angew. Math. 358 (1985) 6-19. | MR 797671 | Zbl 0552.10010
and ,18 S-unit equations and their applications, New Advances in Transcendence Theory (to appear). | MR 971998 | Zbl 0658.10023
, , and ,19 On S-unit equations in two unknowns, Invent. Math. (to appear). | MR 939471 | Zbl 0662.10012
, , and ,20 Explicit upper bounds for the solutions of some Diophantine equations, Ann. Acad. Sc. Fenn. Ser. AI 5 (1980) 3-12. | MR 595172 | Zbl 0402.10018
,21 Effective estimates for the integer solutions of norm form and discriminant form equations, Publ. Math. Debrecen 25 (1978) 311-325. | MR 517016 | Zbl 0394.10010
and ,22 Norm form equations and explicit lower bounds for linear forms with algebraic coefficients, Studies in Pure Math. to the Memory of Paul Turán, Birkhäuser, Basel, pp. 245-257. | MR 820227 | Zbl 0518.10020
and ,23 On prime factors of sums of integers I, Comp. Math. 59 (1986) 81-88. | Numdam | MR 850123 | Zbl 0602.10031
, and ,24 On prime factors of sums of integers III, Acta Arith. (to appear). | MR 932530 | Zbl 0588.10001
, and ,25 An Introduction to the Theory of Numbers, 5th edn., Oxford (1979). | MR 568909 | Zbl 0020.29201
and ,26 On the difference between consecutive primes, Quarterly J. Math. Oxford 8 (1937) 255-266. | JFM 63.0903.04 | Zbl 0017.38904
,27 Integral points on curves, Publ. Math. I.H.E.S. 6 (1960) 27-43. | Numdam | MR 130219 | Zbl 0112.13402
,28 On the representations of integers by binary forms, Acta Arith. 6 (1960) 333-363. | MR 120195 | Zbl 0102.03601
and ,29 On the numerical solution of a differential - difference equation arising in analytic number theory, Math. Comp. 23 (1969) 417-421. | MR 247789 | Zbl 0176.46602
and ,30 Zur Approximation algebraischer Zahlen, I: Über den grössten Primteiler binärer Formen, Math. Ann. 107 (1933) 691-730. | JFM 59.0220.01 | MR 1512822 | Zbl 0006.10502
,31 Zur Approximation algebraischer Zahlen, II: Über die Anzahl der Darstellungen grösser Zahlen durch binäre Formen, Math. Ann. 108 (1933) 37-55. | JFM 59.0220.01 | MR 1512833 | Zbl 0006.15604
,32 On the lattice points on curves of genus 1, Proc. London Math. Soc. (2) 39 (1935) 431-466. | JFM 61.0146.02 | Zbl 0012.15006
,33 On Thue's equation, Math. Scand. 55 (1984) 188-200. | Zbl 0544.10014
,34 Chains of large gaps between consecutive primes, Adv. in Math. 39 (1981) 257-269. | MR 614163 | Zbl 0457.10023
,35 Numbers with small prime factors, and the least k-th power non-residue, Memoirs of the American Math. Soc. 106 (1971). | MR 286739 | Zbl 0211.37801
,36 On divisors of sums of integers I, Acta Math. Hungar. 48 (1986) 147-154. | MR 858392 | Zbl 0612.10042
and ,37 On divisors of sums of integers II, J. reine angew. Math. 365 (1986) 171-191. | MR 826157 | Zbl 0578.10045
and ,38 Integer points and the rank of Thue elliptic curves, Invent. Math. 66 (1982) 395-404. | MR 662599 | Zbl 0494.14008
,39 Representations of integers by binary forms and the rank of the Mordell-Weil group, Invent. Math. 74 (1983) 281-292. | MR 723218 | Zbl 0525.14012
,40 Integer points on curves of genus 1, J. London Math. Soc. 28 (1983) 1-7. | MR 703458 | Zbl 0487.10015
,41 Quantitative results in Diophantine geometry, Preprint, M.I.T. (1984).
,42 Estimation of the solutions of the Thue equation (Russian), Izv. Akad. Nauk. SSSR Ser. Mat. 36 (1972) 712-741. | MR 313186
,43 Some remarks on prime divisors of integers, Seminaire de Théorie des Nombres, Paris 1984-85, Progress in Math. 63, Birkhauser, Boston, etc. (1986) 217-223. | MR 897351 | Zbl 0602.10030
,,44 On prime factors of sums of integers II, Diophantine Analysis, LMS Lecture Notes 109, Cambridge Univ. Press (1986) 83-98. | MR 874122 | Zbl 0602.10032
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