On strings of consecutive integers
with no large prime factors

Antal Balog
Mathematical Institute
Budapest 1364
Hungary
e-mail: balog@math-inst.hu
and
Trevor D. Wooley
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

Abstract:

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 $\varepsilon$, we show that there are infinitely many strings of consecutive integers of size about n, free of prime factors exceeding $n^\varepsilon$, with the length of the strings tending to infinity with speed $\log \log \log \log n$.

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© Copyright 1998, Australian Mathematical Society
TeXAdel Scientific Publishing
1998-09-18
TeXAdel Scientific Publishing
1998-09-18