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**

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

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