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25572Trivial theorem

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  • Kermit Rose
    Jul 3, 2014
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      Here is a trivial theorem.

      Every sum of an odd number of  3 or more consecutive odd positive integers is odd and composite.

      1 + 3 + 5 = 9
      3 + 5 + 7 = 15


      Every odd composite positive integer is the sum of an odd number of 3 or more consecutive odd positive integers.

      77 = 5 + 7 + 9 + 11 + 13 + 15 + 17

      Even though the theorem is trivial, it might be useful for proof of difficult theorems
      which relate primes to squares.

      Kermit