Hello

I'm trying to prove the following conjecture,

Any positive integer $\displaystyle n$ can be expressed in the form

$\displaystyle n=\varepsilon _{1}1^2+\varepsilon _22^2+\varepsilon _33^2+...+\varepsilon _mm^2$

where $\displaystyle m$ a positive integer and $\displaystyle \varepsilon _i=1$ or $\displaystyle -1,i=1,2,3,...,m$.

Any ideas ?