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More properties about odd perfect numbers


  • Berdellima, Arian


As shown by Euler an odd perfect number n must be of the form n=p^α m^2 where p≡α≡1 (mod 4) and p is called the special prime. In this work we show that p≥13 and if q∈{3,5} and q|n then either gcd⁡(q,σ(m^2 ))=1 or gcd⁡(q,σ(p^α ))=1.

Suggested Citation

  • Berdellima, Arian, 2011. "More properties about odd perfect numbers," MPRA Paper 31587, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31587

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    More about this item


    perfect numbers; odd perfect numbers; special prime; greatest common divisor;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • Z0 - Other Special Topics - - General

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