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Re: Puzzle of sum to composite

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  • 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 1 of 5 , Apr 15, 2012
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      --- 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 2 of 5 , Apr 15, 2012
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        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]
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