References for: Perfect numbers


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Books:

  1. D'Ooge (tr.), Nicomachus, Introduction to arithmetic (New York, 1926).
  2. T L Heath, The thirteen books of Euclid's Elements (New York, 1956).
  3. O V Kuzhel, Development of the concept of number : Divisibility criteria : Perfect numbers (Ukrainian), Vidavnice Obednannja "Visca Skola" (Kiev, 1974).
  4. R Shoemaker, Perfect numbers (Washington, 1973).
  5. A Weil, Number theory : An approach through history (Boston-Basel-Stuttgart, 1984).

Articles:

  1. S Brentjes, Die ersten sieben vollkommenen Zahlen und drei Arten befreundeter Zahlen in einem Werk zur elementaren Zahlentheorie von Ismail b. Ibrahim ibn Fallus, NTM Schr. Geschichte Natur. Tech. Medizin 24 (1) (1987), 21-30.
  2. S Brentjes, Eine Tabelle mit vollkommenen Zahlen in einer arabischen Handschrift aus dem 13. Jahrhundert, Nieuw Arch. Wisk. (4) 8 (2) (1990), 239-241.
  3. M Crubellier and J Sip, Looking for perfect numbers, History of Mathematics : History of Problems (Paris, 1997), 389-410.
  4. S Drake, The rule behind "Mersenne's numbers", Physis-Riv. Internaz. Storia Sci. 13 (4) (1971), 421-424.
  5. N Miura, Charles de Bovelles and perfect numbers, Historia Sci. No. 34 (1988), 1-10.
  6. K P Moesgaard, Tychonian observations, perfect numbers, and the date of creation : Longomontanus's solar and precessional theories, J. Hist. Astronom. 6 (1975), 84-99.
  7. M L Nankar, History of perfect numbers, Ganita Bharati 1 (1-2) (1979), 7-8.
  8. Perfect numbers and imperfect mathematicians (Persian), Bull. Iranian Math. Soc. 9 (1) (1981/82), 84-79.
  9. E Picutti, Pour l'histoire des sept premiers nombres parfaits, Historia Math. 16 (2) (1989), 123-136.
  10. R Rashed, Ibn al-Haytham et les nombres parfaits, Historia Math. 16 (4) (1989), 343-352.
  11. T N Sinha, Perfect numbers as a source of fundamentals of number theory, Math. Ed. 5 (2) (1989), 82-89.
  12. C M Taisbak, Perfect numbers : A mathematical pun? An analysis of the last theorem in the ninth book of Euclid's Elements, Centaurus 20 (4) (1976), 269-275.
  13. H S Uhler, A brief history of the investigations on Mersenne numbers and the latest immense primes, Scripta Math. 18 (1952), 122-131.
  14. A M Vaidya, Comment on : "History of perfect numbers", Ganita Bharati 1 (3-4) (1979), 22.
  15. S Wagon, Perfect numbers, Math. Intelligencer 7 (2) (1985), 66-68.

JOC/EFR May 2009

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