منابع مشابه
Maximum Gcd among Pairs of Random Integers
Fix α > 0, and sample N integers uniformly at random from { 1, 2, . . . , ⌊ eαN ⌋} . Given η > 0, the probability that the maximum of the pairwise GCDs lies between N2−η and N2+η converges to 1 as N → ∞. More precise estimates are obtained. This is a Birthday Problem: two of the random integers are likely to share some prime factor of order N2 / log(N). The proof generalizes to any arithmetical...
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A probabilistic algorithm is exhibited that calculates the gcd of many integers using gcds of pairs of integers; the expected number of pairwise gcds required is less than two.
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where θ = 1 + √ d 2 if d mod 4 = 1 and θ = √ d if d mod 4 = 2, 3. The purpose of this paper is to compute the extended gcd of to quadratic integers in ring Z[θ]. We assume throughout that Z[θ] is principal ideal ring, but not necessarily an euclidean ring. If [a, b+ cθ] is the module {ax+(b+ cθ)y, x, y ∈ Z}, it can be shown [3] that I is an ideal of Z[θ] if and only if I = [a, b+ cθ]; where a, ...
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We give an l-ary greatest common divisor algorithm in the ring of integers of any number field with class number 1, i.e., factorial rings of integers. The algorithm has a quadratic running time in the bit-size of the input using naive integer arithmetic.
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The reversal of a positive integer A is the number obtained by reading A backwards in its decimal representation. A pair (A,B) of positive integers is said to be palindromic if the reversal of the product A × B is equal to the product of the reversals of A and B. A pair (A,B) of positive integers is said to be polynomial if the product A×B can be performed without carry. In this paper, we use p...
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ژورنال
عنوان ژورنال: Integers
سال: 2011
ISSN: 1867-0652
DOI: 10.1515/integ.2011.006