Question 1
A1 (SLO) Let $a,b,$ and $c$ be positive real numbers such that $abc=1$. Prove that
$$\frac{ab}{a^5+b^5+ab}+\frac{bc}{b^5+c^5+bc}+\frac{ca}{c^5+a^5+ca}\le1.$$
When does equality hold?
$$\frac{ab}{a^5+b^5+ab}+\frac{bc}{b^5+c^5+bc}+\frac{ca}{c^5+a^5+ca}\le1.$$
When does equality hold?