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1996 | 74 | 4 | 365-385
Tytuł artykułu

On the number of prime factors of integers of the form ab + 1

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
74
Numer
4
Strony
365-385
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-07-10
poprawiono
1995-09-07
Twórcy
autor
  • Mathematical Institute, Kossuth Lajos University, 4010 Debrecen, Hungary
autor
  • Mathematical Institute, Hungarian Academy of Sciences, H-1053 Budapest, Hungary
  • Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Bibliografia
  • [1] E. R. Canfield, P. Erdős and C. Pomerance, On a problem of Oppenheim concerning 'Factorisatio Numerorum', J. Number Theory 17 (1983), 1-28.
  • [2] H. Davenport, Multiplicative Number Theory, 2nd ed., Graduate Texts in Math. 74, Springer, 1980.
  • [3] P. Erdős, C. Pomerance, A. Sárközy and C. L. Stewart, On elements of sumsets with many prime factors, J. Number Theory 44 (1993), 93-104.
  • [4] P. Erdős, C. L. Stewart and R. Tijdeman, Some diophantine equations with many solutions, Compositio Math. 66 (1988), 37-56.
  • [5] P. Erdős and P. Turán, On a problem in the elementary theory of numbers, Amer. Math. Monthly 41 (1934), 608-611.
  • [6] J.-H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584.
  • [7] J.-H. Evertse, The number of solutions of decomposable form equations, to appear.
  • [8] J.-H. Evertse and K. Győry, Finiteness criteria for decomposable form equations, Acta Arith. 50 (1988), 357-379.
  • [9] P. X. Gallagher, The large sieve, Mathematika 14 (1967), 14-20.
  • [10] K. Győry, On the numbers of families of solutions of systems of decomposable form equations, Publ. Math. Debrecen 42 (1993), 65-101.
  • [11] K. Győry, Some applications of decomposable form equations to resultant equations, Colloq. Math. 65 (1993), 267-275.
  • [12] K. Győry, C. L. Stewart and R. Tijdeman, On prime factors of sums of integers I, Compositio Math. 59 (1986), 81-88.
  • [13] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, 1979.
  • [14] C. Pomerance, A. Sárközy and C. L. Stewart, On divisors of sums of integers III, Pacific J. Math. 133 (1988), 363-379.
  • [15] A. Sárközy, Hybrid problems in number theory, in: Number Theory, New York 1985-88, Lecture Notes in Math. 1383, Springer, 1989, 146-169.
  • [16] A. Sárközy, On sums a + b and numbers of the form ab + 1 with many prime factors, Grazer Math. Ber. 318 (1992), 141-154.
  • [17] A. Sárközy and C. L. Stewart, On divisors of sums of integers V, Pacific J. Math. 166 (1994), 373-384.
  • [18] A. Sárközy and C. L. Stewart, On prime factors of integers of the form ab + 1, to appear.
  • [19] H. P. Schlickewei, S-unit equations over number fields, Invent. Math. 102 (1990), 95-107.
  • [20] H. P. Schlickewei, The quantitative Subspace Theorem for number fields, Compositio Math. 82 (1992), 245-273.
  • [21] W. M. Schmidt, The subspace theorem in diophantine approximations, Compositio Math. 69 (1989), 121-173.
  • [22] C. L. Stewart, Some remarks on prime divisors of sums of integers, in: Séminaire de Théorie des Nombres, Paris, 1984-85, Progr. Math. 63, Birkhäuser, 1986, 217-223.
  • [23] C. L. Stewart and R. Tijdeman, On prime factors of sums of integers II, in: Diophantine Analysis, J. H. Loxton and A. J. van der Poorten (eds.), Cambridge University Press, 1986, 83-98.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav74i4p365bwm
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