- 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 - On Sunday, April 15, 2012, Kermit Rose <kermit@...> wrote:
> Prove that every positive composite integer can be expressed as a sum of

N=ab=(p+q)(r+s)=pr+ps+qr+qs

> 4 positive integers

> such that the product of the 4 positive integers is a square integer.

pr * ps * qr * qs = ( pqrs )^2

otherwise said, /any/ decomposition of the two factors of N into a sum

leads to a decomposition satisfying your constraints.

Nice Sunday to all of you,

Maximilian

[Non-text portions of this message have been removed] - 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] - --- In primenumbers@yahoogroups.com, Kermit Rose <kermit@...> wrote:
>

--every positive integer is a sum of 4 squares (Fermat, Euler, Lagrange);

> 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

the product of 4 squares is a square.

QED.

Note the word "composite" was not required. - 2012. �prilis 16. 2:00 WarrenS �rta, <warren.wds@...>:

> **

Missed the condition that here the 4 terms should be positive, and in the

>

>

>

>

> --- 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.

>

>

>

Lagrange's theorem you can use 0 as a term.

[Non-text portions of this message have been removed]