Loading ...
Sorry, an error occurred while loading the content.

Re: Puzzle of sum to composite

Expand Messages
  • Robert Gerbicz
    You can also generalize the problem for non-composites, the only exceptions are N=1,2,3,5, for the other cases these are good decompositions:
    Message 1 of 5 , Apr 15, 2012
    • 0 Attachment
      You can also generalize the problem for non-composites, the only exceptions
      are N=1,2,3,5, for the other cases these are good decompositions:
      2n=1+1+(n-1)+(n-1)
      2n+1=1+4+(n-2)+(n-2)


      [Non-text portions of this message have been removed]
    • WarrenS
      ... --every positive integer is a sum of 4 squares (Fermat, Euler, Lagrange); the product of 4 squares is a square. QED. Note the word composite was not
      Message 2 of 5 , Apr 15, 2012
      • 0 Attachment
        --- In primenumbers@yahoogroups.com, Kermit Rose <kermit@...> wrote:
        >
        > Hello Friends.
        >
        > Prove that every positive composite integer can be expressed as a sum of
        > 4 positive integers
        > such that the product of the 4 positive integers is a square integer.
        >
        > Kermit


        --every positive integer is a sum of 4 squares (Fermat, Euler, Lagrange);
        the product of 4 squares is a square.
        QED.

        Note the word "composite" was not required.
      • Robert Gerbicz
        ... Missed the condition that here the 4 terms should be positive, and in the Lagrange s theorem you can use 0 as a term. [Non-text portions of this message
        Message 3 of 5 , Apr 15, 2012
        • 0 Attachment
          2012. �prilis 16. 2:00 WarrenS �rta, <warren.wds@...>:

          > **
          >
          >
          >
          >
          > --- In primenumbers@yahoogroups.com, Kermit Rose <kermit@...> wrote:
          > >
          > > Hello Friends.
          > >
          > > Prove that every positive composite integer can be expressed as a sum of
          > > 4 positive integers
          > > such that the product of the 4 positive integers is a square integer.
          > >
          > > Kermit
          >
          > --every positive integer is a sum of 4 squares (Fermat, Euler, Lagrange);
          > the product of 4 squares is a square.
          > QED.
          >
          > Note the word "composite" was not required.
          >
          >
          >
          Missed the condition that here the 4 terms should be positive, and in the
          Lagrange's theorem you can use 0 as a term.


          [Non-text portions of this message have been removed]
        Your message has been successfully submitted and would be delivered to recipients shortly.