caa a22 4500 388047038 CHVBK 20180307125041.0 cr unu---uuuuu 161130e199804 xx s 000 0 eng 10.1017/S1446788700001750 doi S1446788700001750 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700001750 On strings of consecutive integers with no large prime factors [Elektronische Daten] We investigate conditions which ensure that systems of binomial polynomials with integer coefficients are simultaneously free of large prime factors. In particular, for each positive number ε, we show that there are infinitely many strings of consecutive integers of size about n, free of prime factors exceeding nε, with the length of the strings tending to infinity with speed log log log log n. Copyright © Australian Mathematical Society 1998 primary 11N25 nationallicence 11B25 nationallicence Smooth numbers nationallicence consecutive integers nationallicence sequences nationallicence Balog Antal E-mail: balog@math-inst.hu Wooley Trevor D. Department of Mathematics University of Michigan East Hall 525 East University Avenue Ann Arbor, Michigan 48109-1109 USA e-mail: wooley@math.lsa.umich.edu Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 266-276 1446-7887 64:2<266 1998 64 JAZ https://doi.org/10.1017/S1446788700001750 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700001750 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Balog Antal E-mail: balog@math-inst.hu NATIONALLICENCE 700 1- Wooley Trevor D. Department of Mathematics University of Michigan East Hall 525 East University Avenue Ann Arbor, Michigan 48109-1109 USA e-mail: wooley@math.lsa.umich.edu NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 64/2(1998-04), 266-276 1446-7887 64:2<266 1998 64 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge