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The last cipher of perfect numbers

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  • FILIPPO GIORDANO
    Euclid s formula concerning perfect numbers, progressively developed for all values of n -except 1- produces numbers whose last ciphers are cyclic: 6-6-8-0.
    Message 1 of 1 , Jan 2, 2002
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      Euclid's formula concerning perfect numbers, progressively developed for all values of n -except 1- produces numbers whose last ciphers are cyclic: 6-6-8-0.

      n=2, perfect number = 6 - last cipher 6,
      n=3, perfect number = 28- last cipher 8,
      n=4, number = 120- last cipher 0,

      n=5, perfect number = 496- last cipher 6,
      n=6, number = 2016- last cipher 6,
      n=7, perfect number = 8128- last cipher 8,
      n=8, number = 32640- last cipher 0,

      n=9, number = 130816- last cipher 6,
      n=10, number = 523776- last cipher 6,
      n=11, number = 2096128- last cipher 8,
      n=12, number = 8386560- last cipher 0.

      Thus, being p = n always an odd number, all perfect numbers have either 6 or 8 as last ciphers. This way the conjecture about 6 or 8 (of Teone da Smirne) as last numbers is clerly demonstrated.
      Filippo Giordano


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