On the probability that n and f(n) are relatively prime III
نویسندگان
چکیده
منابع مشابه
The Probability that Random Polynomials Are Relatively r-Prime
We find the generating function for the number of k-tuples of monic polynomials of degree n over Fq that are relatively r-prime, meaning they have no common factor that is an rth power. A corollary is the probability that k monic polynomials of degree n are relatively r-prime, which we express in terms of a zeta function for the polynomial ring. This gives an analogue of Benkoski’s result conce...
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The following problem arose in connection with our research in statistical group theory: estimate a, := the number of partitions of n into parts that are pairwise relatively prime. This differs from most problems in the theory of partitions because of the complicated relationship between the part sixes. We obtain an asymptotic formula for log a,, but leave open the challenging task of obtaining...
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Let a and b be two polynomials having numerical coeecients. We consider the question: when are a and b relatively prime? Since the coeecients of a and b are approximant, the question is the same as: when are two polynomials relatively prime, even after small perturbations of the coeecients? In this paper we provide a numeric parameter for determining that two polynomials are prime, even under s...
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A nonempty finite set of positive integers A is relatively prime if gcd(A) = 1 and it is relatively prime to n if gcd(A ∪ {n}) = 1. The number of nonempty subsets of A which are relatively prime to n is Φ(A,n) and the number of such subsets of cardinality k is Φk(A,n). Given positive integers l1, l2, m2, and n such that l1 ≤ l2 ≤ m2 we give Φ([1,m1] ∪ [l2,m2], n) along with Φk([1,m1] ∪ [l2,m2],...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1972
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-20-3-267-289