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On strings of consecutive integers with no large prime factors

Published online by Cambridge University Press:  09 April 2009

Antal Balog
Affiliation:
Mathematical Institute Budapest1364Hungary e-mail: balog@math-inst.hu
Trevor D. Wooley
Affiliation:
Department of Mathematics University of Michigan East Hall525 East University Avenue Ann Arbor, Michigan 48109-1109USA e-mail: wooley@math.lsa.umich.edu
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1998

References

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