Question 165
Let $a$ and $b$ be two integers. Prove that the number:
$$
\prod_{k=1}^{n-1} \left( a^2 + b^2 + 1 - 2a \cos \frac{2k\pi}{n} - 2b \sin \frac{2k\pi}{n} \right)
$$
is a positive integer and it can be written as the sum of two perfect squares.
$$
\prod_{k=1}^{n-1} \left( a^2 + b^2 + 1 - 2a \cos \frac{2k\pi}{n} - 2b \sin \frac{2k\pi}{n} \right)
$$
is a positive integer and it can be written as the sum of two perfect squares.