nAalniaOMliO wrote: Let $f(x)$ be a linear function and $k,l,m$ - pairwise different real numbers. It is known that $f(k)=l^3+m^3$, $f(l)=m^3+k^3$ and $f(m)=k^3+l^3$. Find the value of $k+l+m$. Let $s=k^3+l^3+m^3$ and the polynomial $p=X^3+f(X)-s$, then $p$ has three distinct real roots $k, l, m$ $\implies$ $(X-l)(X-k)(X-m)=p$ $\implies$ $k+l+m=-[X^2]p=0$