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Mathematics of Computation

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Computation of all the amicable pairs below $ 10\sp {10}$

Author: H. J. J. te Riele
Journal: Math. Comp. 47 (1986), 361-368, S9
MSC: Primary 11A25; Secondary 11Y70
MathSciNet review: 842142
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Abstract: An efficient exhaustive numerical search method for amicable pairs is described. With the aid of this method all 1427 amicable pairs with smaller member below $ {10^{10}}$ have been computed, more than 800 pairs being new. This extends previous exhaustive work below $ {10^8}$ by H. Cohen. In three appendices (contained in the supplements section of this issue), various statistics are given, including an ordered list of all the gcd's of the 1427 amicable pairs below $ {10^{10}}$ (which may be useful in further amicable pair research). Suggested by the numerical results, a theorem of Borho and Hoffmann for constructing APs has been extended.

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Keywords: Amicable pair
Article copyright: © Copyright 1986 American Mathematical Society

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