On Thabit ibn Kurrah’s formula for amicable numbers

Borho, Walter

doi:10.1090/S0025-5718-1972-0313177-4

On Thabit ibn Kurrah’s formula for amicable numbers
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Math. Comp. 26 (1972), 571-578 Request permission

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.

References

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