An integer
is called Silesian if there exist positive integers
such that ![n = \frac{a^2+b^2+c^2}{ab+bc+ca}](/media/m/a/0/4/a04102d9241e6c3d04154000cbebea4c.png)
a) Prove that there are infinitely many Silesian integers.
b) Prove that not all positive integers are Silesian.
An integer $n$ is called \emph{Silesian} if there exist positive integers $a, b, c$ such that
$$n = \frac{a^2+b^2+c^2}{ab+bc+ca}$$
a) Prove that there are infinitely many Silesian integers.
b) Prove that not all positive integers are Silesian.