On a problem of Oppenheim concerning “factorisatio numerorum”
@article{Canfield1983OnAP, title={On a problem of Oppenheim concerning “factorisatio numerorum”}, author={E. Rodney Canfield and Paul Erd{\"o}s and Carl Pomerance}, journal={Journal of Number Theory}, year={1983}, volume={17}, pages={1-28} }
344 Citations
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A rigorous time bound for factoring integers
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In this paper a probabilistic algorithm is exhibited that factors any positive integer n into prime factors in expected time at most Ln[2, 1 + o()] for n oo, where L,[a, b] = exp(b(logx)a(loglogx)l…
Order computations in generic groups
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It is proved that a generic algorithm can compute |α| for all α ∈ S ⊆ G in near linear time plus the cost of a single order computation with N = λ(S), and it is shown that in most cases the structure of an abelian group G can be determined using an additional O (Nδ/4 ) group operations, given an O ( Nδ ) bound on |G| = N.
The least common multiple of sets of positive integers
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Motivated by the problem of estimating log lcm{f(k) : 1 ≤ f(k) ≤ n} when f is a polynomial, we study the typical behavior of the logarithm of the least common multiple of sets of integers in {1, . .…
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