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

• Autorzy: K. Győry , A. Sárközy , C. L. Stewart
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 74
• Numer: 4
• Strony: 365-385

Daty

wydano

1996

otrzymano

1995-07-10

poprawiono

1995-09-07

Twórcy

autor

K. Győry

• Mathematical Institute, Kossuth Lajos University, 4010 Debrecen, Hungary

autor

A. Sárközy

• Mathematical Institute, Hungarian Academy of Sciences, H-1053 Budapest, Hungary

autor

C. L. Stewart

• 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.