Consider the number 3600. It is very special, because
Similarly, we find that 88201 = 992 + 2802 = 2872 + 2542 = 2832 + 3522 = 1972 + 7842.
In 1747, Euler proved which numbers are representable as a sum of two squares. We are interested in the numbers n which admit representations of all of the following four types:
where the ak and bk are positive integers.
There are 75373 such numbers that do not exceed 107.
How many such numbers are there that do not exceed 2109?