- Thread starter
- #1

#### melese

##### Member

- Feb 24, 2012

- 27

(

A related question of my own, but I don't have/know the answer:

If $\deg({f})=d$, then what is the smallest possible value of $n$.

For example: I know that it's $2$, when $d=2$ and $1$ when $d=0$.

መለሰ

**HUN,1979**) Prove the following statement: If a polynomial $f(x)$ with real coefficients takes only nonnegative values, then there exists a positive integer $n$ and polynomials $g_1(x),g_2(x),...,g_n(x)$ such that $f(x)=g_1(x)^2+g_2(x)^2+\cdots+g_n(x)^2$.A related question of my own, but I don't have/know the answer:

If $\deg({f})=d$, then what is the smallest possible value of $n$.

For example: I know that it's $2$, when $d=2$ and $1$ when $d=0$.

መለሰ

Last edited by a moderator: