Short interval results for squarefree numbers
نویسندگان
چکیده
منابع مشابه
Detecting squarefree numbers
We present an algorithm, based on the explicit formula for L-functions and conditional on GRH, for proving that a given integer is squarefree with little or no knowledge of its factorization. We analyze the algorithm both theoretically and practically, and use it to prove that several RSA challenge numbers are not squarefull.
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In this paper we consider the generalized Catalan numbers F (s, n) = 1 (s−1)n+1 ( sn n ) , which we call s-Catalan numbers. We find all natural numbers n such that for p prime, p divides F (p, n), q ≥ 1 and all distinct residues of F (p, n) (mod p), q = 1, 2. As a byproduct we settle a question of Hough and the late Simion on the divisibility of the 4-Catalan numbers by 4. We also prove that ( ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1990
ISSN: 0022-314X
DOI: 10.1016/0022-314x(90)90108-4