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On strings of consecutive integers with no large prime factors
Published online by Cambridge University Press: 09 April 2009
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 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.
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- Copyright © Australian Mathematical Society 1998
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