Four large amicable pairs

Author:
H. J. J. te Riele

Journal:
Math. Comp. **28** (1974), 309-312

MSC:
Primary 10A40; Secondary 10-04

MathSciNet review:
0330033

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Abstract | References | Similar Articles | Additional Information

Abstract: This note gives a report of systematic computer tests of Euler's rule and several Thabit-ibn-Kurrah-rules, in search of large amicable pairs. The tests have yielded four amicable pairs, which are much larger than the largest amicable pair thus far known.

**[1]**J. Alanen, O. Ore, and J. Stemple,*Systematic computations on amicable numbers*, Math. Comp.**21**(1967), 242–245. MR**0222006**, 10.1090/S0025-5718-1967-0222006-7**[2]**Walter Borho,*On Thabit ibn Kurrah’s formula for amicable numbers*, Math. Comp.**26**(1972), 571–578. MR**0313177**, 10.1090/S0025-5718-1972-0313177-4**[3]**Edward Brind Escott,*Amicable numbers*, Scripta Math.**12**(1946), 61–72. MR**0017293****[4]**L. Euler,*De Numeris Amicabilibus*, Leonhardi Euleri Opera Omnia, Teubner, Leipzig and Berlin, Ser. I, vol. 2, 1915, pp. 63-162.**[5]**Mariano García,*New amicable pairs*, Scripta Math.**23**(1957), 167–171. MR**0098703****[6]**Donald E. Knuth,*The art of computer programming. Vol. 2: Seminumerical algorithms*, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont, 1969. MR**0286318****[7]**Elvin J. Lee,*Amicable numbers and the bilinear diophantine equation*, Math. Comp.**22**(1968), 181–187. MR**0224543**, 10.1090/S0025-5718-1968-0224543-9**[8]**Elvin J. Lee and Joseph S. Madachy,*The history and discovery of amicable numbers. I*, J. Recreational Math.**5**(1972), no. 2, 77–93. MR**0446841****[9]**Elvin J. Lee and Joseph S. Madachy,*The history and discovery of amicable numbers. II*, J. Recreational Math.**5**(1972), no. 3, 153–173. MR**0446842****[10]**Elvin J. Lee and Joseph S. Madachy,*The history and discovery of amicable numbers. III*, J. Recreational Math.**5**(1972), no. 4, 231–249. MR**0446843****[11]**D. H. Lehmer,*An extended theory of Lucas’ functions*, Ann. of Math. (2)**31**(1930), no. 3, 419–448. MR**1502953**, 10.2307/1968235**[12]**Hans Riesel,*Lucasian criteria for the primality of 𝑁=ℎ⋅2ⁿ-1*, Math. Comp.**23**(1969), 869–875. MR**0262163**, 10.1090/S0025-5718-1969-0262163-1

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1974-0330033-8

Keywords:
Amicable numbers,
Lucas-Lehmer test

Article copyright:
© Copyright 1974
American Mathematical Society