## When $\frac{a^2}{b+c}＋\frac{b^2}{a+c}＋\frac{c^2}{a+b}$ is integer and $a,b,c$ are coprime natural numbers, is there a solution except (183,77,13)?

Given $a,b,c\in \Bbb{N}$ such that $\{a,b,c\}$ are coprime natural numbers and $a,b,c&gt;1$. When $$\frac{a^2}{b+c}＋\frac{b^2}{c+a}＋\frac{c^2}{a+b}\in\mathbb Z\,?$$ I know the solution \$\{183,77,1...