@article{bwmeta1.element.bwnjournal-article-aav74i4p365bwm,
author = {K. Gy\H ory and A. S\'ark\"ozy and C. L. Stewart},
title = {On the number of prime factors of integers of the form ab + 1},
journal = {Acta Arithmetica},
volume = {76},
year = {1996},
pages = {365-385},
zbl = {0857.11047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav74i4p365bwm}
}
K. Győry; A. Sárközy; C. L. Stewart. On the number of prime factors of integers of the form ab + 1. Acta Arithmetica, Tome 76 (1996) pp. 365-385. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav74i4p365bwm/
[000] [1] E. R. Canfield, P. Erdős and C. Pomerance, On a problem of Oppenheim concerning 'Factorisatio Numerorum', J. Number Theory 17 (1983), 1-28. | Zbl 0513.10043
[001] [2] H. Davenport, Multiplicative Number Theory, 2nd ed., Graduate Texts in Math. 74, Springer, 1980. | Zbl 0453.10002
[002] [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. | Zbl 0780.11040
[003] [4] P. Erdős, C. L. Stewart and R. Tijdeman, Some diophantine equations with many solutions, Compositio Math. 66 (1988), 37-56. | Zbl 0639.10014
[004] [5] P. Erdős and P. Turán, On a problem in the elementary theory of numbers, Amer. Math. Monthly 41 (1934), 608-611. | Zbl 60.0917.05
[005] [6] J.-H. Evertse, On equations in S-units and the Thue-Mahler equation, Invent. Math. 75 (1984), 561-584. | Zbl 0521.10015
[006] [7] J.-H. Evertse, The number of solutions of decomposable form equations, to appear. | Zbl 0886.11015
[007] [8] J.-H. Evertse and K. Győry, Finiteness criteria for decomposable form equations, Acta Arith. 50 (1988), 357-379. | Zbl 0595.10013
[008] [9] P. X. Gallagher, The large sieve, Mathematika 14 (1967), 14-20. | Zbl 0163.04401
[009] [10] K. Győry, On the numbers of families of solutions of systems of decomposable form equations, Publ. Math. Debrecen 42 (1993), 65-101. | Zbl 0792.11004
[010] [11] K. Győry, Some applications of decomposable form equations to resultant equations, Colloq. Math. 65 (1993), 267-275. | Zbl 0820.11018
[011] [12] K. Győry, C. L. Stewart and R. Tijdeman, On prime factors of sums of integers I, Compositio Math. 59 (1986), 81-88. | Zbl 0602.10031
[012] [13] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford University Press, 1979. | Zbl 0423.10001
[013] [14] C. Pomerance, A. Sárközy and C. L. Stewart, On divisors of sums of integers III, Pacific J. Math. 133 (1988), 363-379. | Zbl 0668.10055
[014] [15] A. Sárközy, Hybrid problems in number theory, in: Number Theory, New York 1985-88, Lecture Notes in Math. 1383, Springer, 1989, 146-169.
[015] [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.
[016] [17] A. Sárközy and C. L. Stewart, On divisors of sums of integers V, Pacific J. Math. 166 (1994), 373-384. | Zbl 0841.11049
[017] [18] A. Sárközy and C. L. Stewart, On prime factors of integers of the form ab + 1, to appear. | Zbl 0960.11045
[018] [19] H. P. Schlickewei, S-unit equations over number fields, Invent. Math. 102 (1990), 95-107. | Zbl 0711.11017
[019] [20] H. P. Schlickewei, The quantitative Subspace Theorem for number fields, Compositio Math. 82 (1992), 245-273. | Zbl 0751.11033
[020] [21] W. M. Schmidt, The subspace theorem in diophantine approximations, Compositio Math. 69 (1989), 121-173. | Zbl 0683.10027
[021] [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.
[022] [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. | Zbl 0602.10032