I found this sum in a book, and it gave the answer without any inkling of a clue as to why it’s correct. Can anyone help me?
Let r(n) be the number of ways n can be written as the sum of two squares of integers that need not be positive, and order is important. For example, r(2)=4 because
sum from n=1 to infinity (-1)^n*r(n)/n.
In other news, I got a new monitor yesterday. Yay!