On Strings of Consecutive Integers with No Large Prime Factors
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چکیده
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 n, with the length of the strings tending to infinity with speed log log log log n. 1991 Mathematics subject classification (Amer. Math. Soc.): primary 11N25, 11B25.
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تاریخ انتشار 1998