On the probability that n and f(n) are relatively prime
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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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: 1970
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-17-2-169-183