Question 103
An integer $n$ is called Silesian if there exist positive integers $a, b$ and $c$ 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 every positive integer is Silesian.
$$
n = \frac{a^{2} + b^{2} + c^{2}}{ab + bc + ca}
$$
a. Prove that there are infinitely many Silesian integers.
b. Prove that not every positive integer is Silesian.