Let us consider the function
and integrate it along a quadratic counterclockwise contour with vertices where is a big odd natural number. Hence,
We note that and that .
It’s also easy to see that
Hence, as we have that
By Residue theorem we have that
It is straightforward to show that
in the limit . The result follows.
Let and . Show that
We note that
In a triangle it holds that
Prove that in any triangle it holds that
Let denote the greatest prime factor of . For example , . Define . Examine if the sum