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Mathematics of Computation

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On Thabit ibn Kurrah's formula for amicable numbers

Author: Walter Borho
Journal: Math. Comp. 26 (1972), 571-578
MSC: Primary 10A40
MathSciNet review: 0313177
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Abstract: This note describes some methods for deriving explicit formulas for amicable numbers which are similar to Thabit's famous rule. The search for new amicable pairs by such rules consists merely in primality tests for certain big numbers. Only two new pairs are actually given, demonstrating the usefulness of the results and simultaneously illustrating the quite strange form of pairs obtained by this new method. It is proposed to use a computer in order to get more solutions.

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Keywords: Amicable numbers, amicable $ k$-cycles, primality tests
Article copyright: © Copyright 1972 American Mathematical Society